Food for Fork Restaurant Analysis - Case Study Example

Executive Summary Food for Fork restaurant enlisted the services of Nada & Associates Research firm to explore some business decisions with regard to establishing a successful upscale restaurant within the city. The main objective was to find out whether there exists a market for the proposed business. This was in addition to identifying the advertisement planning, location, design and pricing characteristics. The research was carried out within a city whose estimated population is 500,000. Specific demographic and qualitative information was collected from a randomly selected sample of 400 respondents. The results formed the basis of recommendations to the restaurant manager which are briefly presented below; 1. The people in this area usually spend about an average of $19.00 or slightly more for a meal at the restaurant and earn average salaries above $70,000 per year. 2. The elegant décor is more preferred by the people in this area and at the same time, there are significant differences in the preference of string quartet to jazz combo. 3. The married people spend more than the single and other people in restaurant each month and others (divorced and separated people). At the same time, the average monthly expenditure varies across genders 4. There is a weak positive relationship between the newspaper section that one reads and the likelihood of going to a restaurant for meals. 5. The people in Location B are willing to pay more for meals than other Locations (A, D, C) but there is not much difference than Locations (A, D). 6. There is a weak relationship between incomes and expenditures in the restaurants. Meaning that not all the people who have high income will be significantly spend more in restaurant. 7. The results show that only 8.8 percent of the variations in total monthly expenditure is explained by age, income, gender, and expected average price. The report recommends the following decisions points to the restaurant manager; 1. The pricing structure should averagely be around $19.00 with specific focus on the middle income earners that with salaries around $70,000 per year. 2. The interior décor should consist of the elegant décor in addition to the background music featuring mostly string quartet. 3. The menu in the restaurant should take into consideration the married people especially the females as they are likely to spend more than the single and others (divorced and separated people) in restaurant each month. 4. Print and electronic media advertising should be varied across all possible channels as there is a weak positive relationship between the newspaper section that one reads and the likelihood of going to a restaurant for meals. 5. Specific focus should be devoted to the tastes and preferences of the residents in Location A, B and D since results indicates that they are willing to pay more for meals. 6. Since the results show that higher incomes does not necessarily mean increased spending in the restaurants, the restaurant should also have a menu for the low income earners. 7. The restaurant should consider factors such as interior design, discounts, and indoor games as important in influencing total monthly expenditure since the results show that only 8.8 percent of the variations in total monthly expenditure are explained by age, income, gender, and expected average price. In summary, though not exhaustive analyzed, there are some salient trends that emerged from the study and should be further investigated. This include, the drive time to the restaurant, the location of the restaurant on a water front view, the type of dressing that the wait staff should adorn and the menu served especially to the singles that would like to socialize. Table of Contents Executive Summary 2 Table of Contents 5 1. Introduction 9 2. Objectives 9 3. Preliminary Analysis 10 3.1 Average expected price of evening meal 10 3.2 Income of the people surveyed 11 3.3 Amount Spent in restaurant each month 11 3.4 Gender 12 3.5 Marital Status 13 3.6 Age 13 3.7 Décor 14 3.7.1 Simple Décor 14 3.7.2 Elegant Décor 14 3.8 Music 15 3.8.1 Jazz Combo 15 3.8.2 String Quarter 15 3.9 Likelihood of attending 16 3.10 The section of newspaper that read 17 3.11 Postcodes of people surveyed 18 4. Analysis of Results 18 4.1 Is average expected price less that $19.00? 18 4.2 Is average income different from $70,000 19 4.3 Is the preference of elegant to simple décor significant? 20 4.4 Is there difference in expenditure across marital status? 21 4.5 Is jazz combo preferred to string quartet? 22 4.6 Is attendance based on newspaper section read ? 23 4.7 Is there relationship between the Area codes and the average price? 24 4.8 Is there difference in expenditures across gender? 25 4.9 Relationship between income and expenditure 26 4.10 Does expenditure depend on income, gender, age and price 27 5. Conclusion and Summary 28 6. Recommendations 31 7. References 33 8. Appendix A 33 8.1 Amount of meal 33 8.2 Income of the people surveyed 34 8.3 Amount Spent in restaurant each month 35 8.4 Gender 35 8.5 Marital Status 36 8.6 Age 36 8.7 Décor 36 8.7.1 Simple Décor 37 8.7.2 Elegant Décor 37 8.8 Music 37 8.8.1 Jazz Combo 37 8.8.2 String Quarter 38 8.9 Likelihood of attending 38 8.10 The section of newspaper that read 39 8.11 Postcodes of people surveyed 39 9. Appendix B 40 9.1 Hypothesis 1: Average price is not less than $19.00? 40 9.2 Hypothesis 2: Average income is not different from $70,000 40 9.3 Hypothesis 3: Elegant décor is preferred to simple décor. 42 9.4 Hypothesis 4: Expenditure is different across marital groups 42 9.5 Hypothesis 5: Jazz combo is preferred to string quartet 43 9.6 Hypothesis 6: Attendance is based on newspaper section reads 44 9.7 Hypothesis 7: Price is influenced by location 46 9.8 Hypothesis 8: Expenditure varies across gender 46 9.9 Hypothesis 9: Increase in income increases monthly expenditure 47 9.10 Hypothesis 10: What influences variations in monthly expenditures 48 10. Appendix C 49 10.1 Q1 49 10.2 Q2 50 10.3 Q3 50 10.4 Q4 51 10.5 Q5 54 10.6 Q6 55 10.7 Q7 57 10.8 Q8 60 10.9 Q9 60 10.10 Q10 61 1. Introduction This report presents a summary of findings on a market research done on behalf of the Restaurant Manager of Food for Fork Restaurant. The company intends to establish an upscale restaurant within the city whose population is currently estimated at 500,000 people with different tastes and preferences. The general objective of the report is to establish whether there exists a market for the restaurant. More specifically, the report seeks to identify the appropriate promotion channels, to determine a suitable location for the business and finally to examine the design and pricing characteristics of the business. The research within a metropolis of an estimated population of 500,000 was based on survey methodology that involved 400 respondents randomly selected. Data analysis involved the use of Statistical Package for Social Scientists (SPSS). The report is organized as follow; first, a preliminary analysis of the data is presented, then, a discussion and analysis of the results based on the various research questions and hypothesis. Finally, a summary and conclusion of the key findings is made. It is worth noting that some of the output from the analysis has been presented in the appendices section. 2. Objectives The specific objectives of the study are as follows; 1. To identify the appropriate promotion channels for the proposed restaurant, 2. To determine a suitable location for the upscale restaurant business 3. To examine the design and pricing characteristics of the restaurant business. 3. Preliminary Analysis In this section, the preliminary analyses of selected variables are presented. The descriptive analysis for the qualitative data and frequency tables for categorical is used to determine some salient features and characteristics that emerge from the data. 3.1 Average expected price of evening meal The histogram (fig. 1) below indicates the frequency of the expected average prices of evening meals in the restaurant. Fig. 1 Histogram showing expected price of an evening meal In figure 1 above, it can be observed that 50% of the patrons expect the average price of the evening meal to be less than $19.00 (the median). This is consistent with the fact that there are slightly more patrons expecting the meal prices to be less than the mean price of $19.23 as indicated by the skewness which is almost normally distributed. Additionally, the highest price that patrons expect to pay is $39.00 while the lowest price is $1.00. (Refer to Appendix A for output on the measures of location) 3.2 Income of the people surveyed The histogram below shows the annual income of the respondents surveyed. The mean income is $77,087 with 50 percent of the patrons surveyed earning less than $77,000 (median). The incomes ranged from $1,000 the lowest to $161,000 the highest paid individual. Fig 2. Histogram showing the annual salaries of the respondents The figure 2 shows that there are slightly more individuals earning more than $77,000 indicating that though the shape of the distribution of incomes is near normal, the skewness is towards the right. In addition, the box plot in appendix A indicates that there are individuals (outliers) earning far less or more than what the majority earn in a year. (Refer to Appendix A for output on the measures of location). 3.3 Amount Spent in restaurant each month The histogram below shows the total amount of dollars by the respondents surveyed. The mean expenditure is $207.94 with 50 percent of the patrons surveyed spending less than $210 (median). The total expenditure ranged from $101 the lowest, to $307 the highest level of expenditure. Fig.3 Histogram showing total expenditure The figure 3 shows that there are slightly more individuals spending less than $210 per month on meals in the restaurants. This is because the shape of the distribution of incomes is somewhat skewed to the left of the middle value. 3.4 Gender Figure 4: Bar chart showing gender The figure above shows that there are slightly more men than women from the sample. The frequency table in Appendix A indicates that there are 204 men constituting 51 percent of the total sample versus 196 women that constitute 49 percent of the sample. 3.5 Marital Status Fig 5: Barchart showing the marital status The fig 5 above indicates that the number of the married respondents were slightly higher (175, 43.8 percent) compared to the other marital status groups. The number of singles group were 146 constituting 36.5 percent while the number of the separated or divorced respondents were 79 or 19.8 percent of the respondents surveyed. 3.6 Age Fig 6: Histogram indicating age of the respondents The fig 6 above indicates that the mean age of the respondents is 36.61 years with 50 percent of the respondents having age of less than 37 years (median). The ages ranged from 17 years (youngest) to 62 years (oldest). The shape of the distribution is somewhat skewed to the left (-0.092) indicating there were a slightly higher number of respondents below 37 years of age. 3.7 Décor 3.7.1 Simple Décor Fig 7.1: Bar chart for preferring simple décor The above bar chart indicates that the number of respondents that very strongly prefer simple décor is 25 (6.3 percent) compared to 140 (35 percent) that do not very strongly prefer the simple décor. We can conclude that a higher percentage is not in favor of the simple décor within the restaurant. 3.7.2 Elegant Décor In the case of elegant décor, it can be observed from the bar chart below that there is a higher percentage that somewhat prefer elegant décor (131 respondents or 32.8 percent) compared to (21 or 5.3 percent that do not very strongly prefer the elegant décor. In sum, we can conclude that there would be more patrons preferring the elegant décor instead of simple décor. Figure 7.2: Preferring elegant décor 3.8 Music 3.8.1 Jazz Combo The figure 8.1 indicates that the number of potential patrons somewhat and very strongly preferring jazz combo are 29 (7.2 percent) and 36 (9.0 percent) respectively. However, it is worth noting that the number of the potential patrons very strongly not preferring and somewhat preferring jazz combo are 118 (29.5 percent) and 106 (26.5 percent) respectively. Figure 8.1 Preferring Jazz Combo 3.8.2 String Quarter Figure 8.2: Preferring string quartet The figure 8.2 indicates that the number of potential patrons that somewhat and very strongly prefer string quartet are 65 (16.3 percent) and 178 (44.5 percent) respectively. However, the number of the potential patrons very strongly not preferring and somewhat preferring string quartet are 36 (9.0 percent) and 82 (20.5 percent) respectively. 3.9 Likelihood of attending Figure 9: Bar chart showing the likelihood of attending The number of patrons that are very unlikely to attend a new restaurant are 78 (19.5 percent), while the number of those that are somewhat unlikely are 76 (19.0 percent). However, the number of those that are undecided constitute a total of 160 (40 percent), whereas the number of patrons very likely to attend a new restaurant in the city are 86 (21.5 percent). This indicates that with strong advertising and better services at the restaurant there is likely to be a higher turnout at the restaurant. 3.10 The section of newspaper that read Figure 10: Barchart showing the section of newspaper that one reads The results indicate that 112 or 28 percent of the respondents read mostly the business section of the newspaper. This is followed by the editorial section, which attracts 104 (26 percent of the respondents). The local and the classified sections have 94 (23.5 percent) and 90 (22.5 percent) of the respondents frequenting it respectively. 3.11 Postcodes of people surveyed Figure 11: Postcodes of people surveyed. The bar chart show that most respondents were residents of the area code B (3, 4, & 5) 109 (27.3 percent) of the respondents. Moreover, 104 (26.0 percent) residents indicated that they were residents of area code D (10, 11, & 12) while area codes A and C had 93 (23.3 percent) and 94 (23.5 percent) respectively of the respondent residing in them. 4. Analysis of Results In this section, key findings of the study are presented, analyzed and discussed. This involves stating the research question, hypothesis testing and interpreting the results that form the basis of conclusions made in this study. 4.1 Is average expected price less that $19.00? In this section, we determine if the average amount that people are willing to pay for a meal is significantly less than the forecast value of $19 obtained from the break even analysis. Hypothesis testing H0: The mean of the payment for meal is the same as of the forecast value of 19$. Average of payment for the meal = 19$. Ha: The mean of the payment for the meal is less than 19$ Average of payment for the meal < 19$. The one-sample t-test was conducted to determine if people are willing to pay a price that is significantly different from the forecasted value of $19.00. The test assumes the following conditions; 1. Independent Assumption 2. Randomization Condition 3. Nearly Normal Condition or normality assumption The results indicate that the mean meal price that people are willing to pay was not significantly different from the forecasted value of $19.00 (t=0.609, p=0.543). Therefore we fail to reject the null hypothesis since p=0.543 > 0.05, and conclude that the people in this area usually spend about an average of $19.00 or slightly more for a meal at the restaurant 4.2 Is average income different from $70,000 The research question seeks to establish if the average income of the people surveyed is significantly different from $70,000. Hypothesis testing H0: average income of the people surveyed = 70,000 Ha: average income of the people surveyed ≠ 70,000 The one sample t-test will be used to determine the average income of the people surveyed earned salary at least $70000 per year. The test compares the sample mean to a known value which in our case is the population mean. The following conditions were assumed; 1. Independent Assumption 2. Randomization Condition 3. Nearly Normal Condition or normality assumption The results indicate that the average income had a statistically significant difference between the sample data and the hypothesized value (t=4.905 , p=0.000). Therefore we reject the null hypothesis since p=0.000 < 0.05 and conclude that the average incomes are significantly different from $70,000. The average income of the people surveyed in the metro area was significantly more than $70,000 with an average of $77,087.5. Therefore, the people in this area earn an average salary not less than $70,000 per year so that they had sufficient disposal income to eat at high-class restaurant (Appendix B). 4.3 Is the preference of elegant to simple décor significant? The question seeks to establish if generalizations can be made about the people in the area as to what they prefer most for the interior décor when presented with a choice between elegant décor and simple décor. Hypothesis testing Paired samples t-Test will be used to test the following hypothesis: H0: mean of preference for simple décor = mean of preference for elegant décor Ha: mean of preference for simple décor ≠ mean of preference for elegant décor To test if there exist significant differences in preferences for the elegant décor to simple décor, a paired samples t-test was used. The test compares the mean scores of two dependent groups or pairs when data on the same case is used in different circumstances. The following assumptions were made; 1. Pairded Data Assumption 2. Randomization Condition 3. Independent Assumption In this sample of 400 people, the average preference of elegant decor was higher (Mean=3.64) than the mean for average preference of simple décor (Mean=2.26). This difference is significant (p=0.000). The null hypothesis is rejected suggesting that the elegant décor is recommended to use in the restaurant because it is more preferred from the people in this area. 4.4 Is there difference in expenditure across marital status? The research question seeks to establish if the spending pattern in the restaurant differs between the married, singles and others (separated and divorced). Hypothesis testing H0: Average spending in restaurant per month for married = singles = other (Divorced, Widow, etc.) Ha: At least one marital group’s expenditure is significantly different To test this hypothesis, an ANOVA test was conducted. The ANOVA test is used to check for the difference in the mean score of more than two groups in one categorical variable. For instance, there are three marital groups (singles, married and the divorced or separated group). The test makes use of the following assumptions; 1. Independence Assumption 2. Equal variance assumption 3. Normal Population Assumption: From the analysis of the statistic output, there are evidence of significant difference in average amount of spending each month across people with different marital status. A tukey post hoc test indicated that married people have significantly most amount spending per month (mean=$232.611, p=0.000) (see SPSS results in appendix B) than the single people with spending (mean=$180.89, p=0.000) and other (Divorced, Widow) (mean=$203.27, p=0.000). Further, the other people (Divorced, Widow) (mean=$203.27, p-0.000) are significantly larger of average spending than the single people (mean=$180,89, p=0.000). Therefore, the married people spend more than the single and other people in the restaurant each month and other people spend more than single people in restaurant per month. 4.5 Is jazz combo preferred to string quartet? In this question we seek to determine if majority of the people in the area prefer a live jazz combo music or string quartet during the evening meals in the restaurant. Hypothesis testing H0: mean of preference for Jazz combo = mean of preference for string quartet Ha: mean of preference for Jazz combo ≠ mean of preference for string quartet To test this hypothesis, Paired test was conducted. The test compares the mean scores of paired dependent variables when data is the same in different circumstances. The following assumption and condition was checked and satisfied: 1. Paired Data Assumption. 2. Independence Assumption. 3. Normality assumption From the analysis of the statistic output, there is evidence that there is significant difference between the average of the two preference (t=33.5, p=0.000) (see SPSS output appendix B). The average preference of String Quartet (mean=3.39) significantly higher than the average preference of Jazz Combo (mean=2.40). This means that we expect the people in this area to prefer the String Combo music in the restaurant more than Jazz Combo. The test of significance show that the t-calculated is 33.469 (p-value = 0.000 < 0.05 significance level). We reject the null hypothesis and conclude that there are significant differences in preference of string quartet to jazz combo. 4.6 Is attendance based on newspaper section read ? The study also sought to establish if there is a relationship between the likelihood of attending a particular restaurant and the newspaper section that one reads. Hypothesis testing H0: There is no association (relationship) between likehood of attending and the section of the newspaper that is read H1: There is an association between likehood of attending and the section of the newspaper To test this hypothesis, Chi Square test was conducted. This test is used to compare the relationship between the counts in categorical answers provided in two or more independent variables. The following assumptions were made to carry out the test. 1. Counted Data Condition 2. Independence Assumption 3. Sample size assumption From the chi square results, Cramer’s Value, (0. 102, p-value 0.413) indicates that there is a weak positive relationship between the newspaper section and the likelihood of going to a restaurant for meals. 4.7 Is there relationship between the Area codes and the average price? Since the metropolis is consists of different types of residents, the study sought to know if there is any link between the area code and the price that potential patrons from this areas would be willing to pay so as to help in precisely locating the business. Hypothesis testing H0: mean price people in Location A willing to pay for meal = mean price people Location B willing to pay for meal = mean price people in Location C willing to pay for meal = mean price people in Location D willing to pay for meal H1: At least one location has a different mean price To test this hypothesis, an ANOVA test was conducted. This test compares the means of multiple groups. In this case we are comparing the means of the different area codes. The test assumes the following conditions; 1. Independence Assumption 2. Equal variance assumption 3. Normal Population Assumption: From the analysis of the statistic output, there exists enough evidence of significant difference in average amount of meal price that people willing to pay across postcodes (f=3.099, p=0.027) (see SPSS results in appendix B). A Tukey post hoc indicated that people in Location B (postcodes 3,4 & 5) have significantly most amount average meal price of people willing to spend for meal (mean=$20.7523, p=015) (see SPSS results in appendix B) than people in Location C (postcodes 6,7,8 &9) (mean=$17.574). However, there are no significant difference on average between Location B and Location A) (postcodes 1&2) (mean=$19.440, p=0.603) and also between Location B and Location D (postcodes 10, 11&12) (mean=$18.94, p=0.294). Therefore, the people in Location B are willing to pay more for meals than other Locations (A, D, C) but there is not much difference than Locations (A, D). People in Location A are willing to pay for meal on average more than locations (D & C). Further People in Location D are willing to pay for meal on average more than Location (C). 4.8 Is there difference in expenditures across gender? In most cases the spending patterns of the men and women differ especially with regard to spending for meals. The study therefore sought to establish if there are significant differences in the expenditure in the restaurant across gender. Hypothesis testing H0: Average monthly restaurant expenditure for male = Average monthly restaurant expenditure for female H1: Average monthly restaurant expenditure for male ≠ Average monthly restaurant expenditure for female To test this hypothesis, the independent sample t-test was conducted to compare the means of both the males and the females groups. The test, determines whether there are significant differences in means of two variables that are independent of each other. The following assumptions were made; 1. Independence Assumption 2. Randomization Condition The results indicate that women’s averagely spend $213.95 than men whose average expenditure is $202.15. Secondly, we test for equality of the means scores between the males and the females and if they are significantly different. From the results, it can be observed that the significance value 0.010 is less than the 0.05 significance level. This indicates that the variances of the male and females are statistically different from each other. We therefore reject the null hypothesis and conclude that the average monthly expenditure varies across genders. 4.9 Relationship between income and expenditure Since the area boasts of having a population with different incomes and standards of living, the study sought to establish if there is any association between the annual income levels and expenditures levels amongst the people living in the area. Hypothesis testing H0: there is no relationship between the income and total expenditure H1: there is a relationship between income and total expenditure To test this hypothesis, the Correlation test was conducted. This test shows the extent to which two or more variables are related or linearly dependent. The test assumes that the following conditions are satisfied. 1. Quantitative Variables Condition 2. Linearity Condition Since the two variables are normally distributed (appendix (B)) so Pearson Correlation (r) test are applied. From the analysis of the statistic output, the results indicate that there is a weak, positive, statistically significant relationship between the two variable (r=0.134, p=0.007). This suggest that the high expenditure in restaurant of the high income salary. However, the relationship was quite weak meaning that not all the people who have high income will be significantly spend more in restaurant. 4.10 Does expenditure depend on income, gender, age and price The study sought to establish if changes in total expenditure by the people in this area are explained by gender, income levels, age, and average price the patrons expect to pay in the restaurant. Hypothesis testing H0: total spend on food each month is not explained by the average price, age, marital status, gender and income. H1: total spend on food each month is explained by the average price, age, marital status, gender and income. To test this hypothesis, the multiple linear regression was used. The test determines the extent to which changes in a particular independent variable leads to a change in the dependent variable. It also determines whether the variations independent variables explain the changes in the dependent variable. The main assumption when performing the test included the following; 1. Linearity: totspent = β + β1avprice + β2age + β3gender +β4 income + u 2. Random sampling 3. Zero conditional mean Total spent = 2,227.71 + 0.003avprice - 0.230age + 0.119gender +0.116 income + u The results showed that only 8.8 percent of the variations in total monthly expenditure are explained by the model. Based on this fact, we fail to reject the null hypothesis and conclude that the independent variables insufficiently explain the variations in the amount of dollars spent per month by the potential patrons. This implies that a unit increase in price leads to a 0.003units increase in total expenditure per month, while a unit increase in income, leads to a 0.116 increase in total expenditure. 5. Conclusion and Summary This section gives a summary of the conclusions of the study based on the results; 1. The people in this area usually spend about an average of $19.00 or slightly more for a meal at the restaurant. 2. Secondly, the people in this area earn an average salary not less than $70,000 per year. 3. The elegant décor is more preferred to simple décor by the people in this area. 4. The married people spend more than the single and other people in restaurant each month and other people spend more than single people in restaurant per month. 5. There are significant differences in the preference of string quartet to jazz combo. 6. There is a weak positive relationship between the newspaper section and the likelihood of going to a restaurant for meals. 7. The people in Location B are willing to pay more for meals than other Locations (A, D, C) but there is not much difference than Locations (A, D). 8. The average monthly expenditure varies across genders. 9. There is a weak relationship between incomes and expenditures in the restaurants. Meaning that not all the people who have high income will be significantly spend more in restaurant. 10. The results show that only 8.8 percent of the variations in total monthly expenditure is explained by age, income, gender, and expected average price. 6. Recommendations The study recommends the following; Available options from research question Recommendation Is the average amount that people are willing to pay for a meal less than the forecast value of $19? The pricing structure of meals within the restaurant should averagely be $19.00 Does the average income of the people surveyed differ from $70,000? Marketing should target the middle income earners with salaries slightly above $70,000 annually. Is there a difference in preference for simple décor and elegant décor? If so, which is preferred? The interior designed with elegant décor as opposed to simple decor. Is there a difference in the mean amount spent in restaurants each month across people with different marital status? The menu should take into consideration the tastes and preferences of the married people as they are likely to spend more in the restaurant. Is there a difference in the between mean preference for jazz combo and string quartet? The background music during the evening meals should be more of string quartet and less of jazz combo Is there an association between likelihood of attending and the section of the newspaper that is read? The study suggest that the advertisements should be placed on various places of both print and electronic media Is there a difference in average price people are willing to pay for a meal across postcodes? The study suggests that pricing should not focus so much on areas that people lives but on the quality of meals offered. Does the average monthly restaurant expenditure differ across genders? The restaurant should target the women in their marketing and advertisement plan but at the same time offer menus appealing to the men. Is there a relationship between income and total expenditure? The menu offered in the restaurant should have items that are also affordable for the low income earners such as buffets and discounts. Can the average amount people spend on food each month be explained by the average price people are willing to pay for meals, age, marital status, gender and income? Increased expenditure would be influenced by other factors such as design, staff, discounts (3 for the price of 1 meals), and indoor games. 7. References Wooldridge, J. M. (2009). Introductory Econometrics; A modern Approach, South Western CENGAGE Learning pg 60. 8. Appendix A This appendix raw data of the (Frequencies and Descriptive Statistic) 8.1 Amount of meal Descriptives Statistic Std. Error What would you expect an average evening meal to be priced? Mean $19.2300 $0.37797 95% Confidence Interval for Mean Lower Bound $18.4869 Upper Bound $19.9731 5% Trimmed Mean $19.2750 Median $19.0000 Variance 57.145 Std. Deviation $7.55943 Minimum $1.00 Maximum $39.00 Range $38.00 Interquartile Range $11.00 Skewness -.085 .122 Kurtosis -.391 .243 describe the normality of this data 8.2 Income of the people surveyed Descriptives Statistic Std. Error What is your annual salary? Mean 77087.5000 1444.84638 95% Confidence Interval for Mean Lower Bound 74247.0371 Upper Bound 79927.9629 5% Trimmed Mean 76863.8889 Median 77000.0000 Variance 835032424.812 Std. Deviation 28896.92760 Minimum 1000.00 Maximum 161000.00 Range 160000.00 Interquartile Range 36000.00 Skewness .067 .122 Kurtosis .138 .243 8.3 Amount Spent in restaurant each month Descriptives Statistic Std. Error How many total dollars do you spend per month in restaurants (for your meals only)? Mean $207.9400 $2.00597 95% Confidence Interval for Mean Lower Bound $203.9964 Upper Bound $211.8836 5% Trimmed Mean $208.1917 Median $210.0000 Variance 1609.570 Std. Deviation $40.11945 Minimum $101.00 Maximum $307.00 Range $206.00 Interquartile Range $58.50 Skewness -.092 .122 Kurtosis -.349 .243 The observed values and the expected values are closely following the straight line, indicating that the normality assumption has been fulfilled. 8.4 Gender What is your gender? Frequency Percent Valid Percent Cumulative Percent Valid Male 204 51.0 51.0 51.0 Female 196 49.0 49.0 100.0 Total 400 100.0 100.0 8.5 Marital Status What is your marital status? Frequency Percent Valid Percent Cumulative Percent Valid Single 146 36.5 36.5 36.5 Married 175 43.8 43.8 80.3 Other (Divorced, Widow, etc.) 79 19.8 19.8 100.0 Total 400 100.0 100.0 8.6 Age Descriptives Statistic Std. Error age Mean 36.61 .445 95% Confidence Interval for Mean Lower Bound 35.73 Upper Bound 37.48 5% Trimmed Mean 36.60 Median 37.00 Variance 79.242 Std. Deviation 8.902 Minimum 17 Maximum 62 Range 45 Interquartile Range 13 Skewness -.037 .122 Kurtosis -.307 .243 8.7 Décor 8.7.1 Simple Décor Prefer Simple Decor Frequency Percent Valid Percent Cumulative Percent Valid Very Strongly Not Prefer 140 35.0 35.0 35.0 Somewhat Not Prefer 107 26.8 26.8 61.8 Neither Prefer Nor Not Prefer 88 22.0 22.0 83.8 Somewhat Prefer 40 10.0 10.0 93.8 Very Strongly Prefer 25 6.3 6.3 100.0 Total 400 100.0 100.0 8.7.2 Elegant Décor Prefer Elegant Decor Frequency Percent Valid Percent Cumulative Percent Valid Very Strongly Not Prefer 21 5.3 5.3 5.3 Somewhat Not Prefer 58 14.5 14.5 19.8 Neither Prefer Nor Not Prefer 78 19.5 19.5 39.3 Somewhat Prefer 131 32.8 32.8 72.0 Very Strongly Prefer 112 28.0 28.0 100.0 Total 400 100.0 100.0 8.8 Music 8.8.1 Jazz Combo Prefer Jazz Combo Frequency Percent Valid Percent Cumulative Percent Valid Very Strongly Not Prefer 118 29.5 29.5 29.5 Somewhat Not Prefer 106 26.5 26.5 56.0 Neither Prefer Nor Not Prefer 111 27.8 27.8 83.8 Somewhat Prefer 29 7.2 7.2 91.0 Very Strongly Prefer 36 9.0 9.0 100.0 Total 400 100.0 100.0 8.8.2 String Quarter Prefer String Quartet Frequency Percent Valid Percent Cumulative Percent Valid Very Strongly Not Prefer 36 9.0 9.0 9.0 Somewhat Not Prefer 82 20.5 20.5 29.5 Neither Prefer Nor Not Prefer 39 9.8 9.8 39.3 Somewhat Prefer 178 44.5 44.5 83.8 Very Strongly Prefer 65 16.3 16.3 100.0 Total 400 100.0 100.0 8.9 Likelihood of attending How likely would it be for you to patronize this restaurant (new upscale restaurant)? Frequency Percent Valid Percent Cumulative Percent Valid Very Unlikely 78 19.5 19.5 19.5 Somewhat Unlikely 76 19.0 19.0 38.5 Neither Likely Nor Unlikely 80 20.0 20.0 58.5 Somewhat Likely 80 20.0 20.0 78.5 Very Likely 86 21.5 21.5 100.0 Total 400 100.0 100.0 8.10 The section of newspaper that read Which section of the local newspaper would you say you read most frequently? Frequency Percent Valid Percent Cumulative Percent Valid Editorial 104 26.0 26.0 26.0 Business 112 28.0 28.0 54.0 Local 94 23.5 23.5 77.5 Classifieds 90 22.5 22.5 100.0 Total 400 100.0 100.0 8.11 Postcodes of people surveyed Please check the letter that includes the Post Code in which you live (coded by letter). Frequency Percent Valid Percent Cumulative Percent Valid A (1 & 2) 93 23.3 23.3 23.3 B (3, 4, & 5) 109 27.3 27.3 50.5 C (6, 7, 8, & 9) 94 23.5 23.5 74.0 D (10, 11, & 12) 104 26.0 26.0 100.0 Total 400 100.0 100.0 9. Appendix B This section checks if the assumption for each test discussed in the study have been satisfied: 9.1 Hypothesis 1: Average price is not less than $19.00? The test assumes the following conditions; 1. Independent Assumption: we have no reason to believe that the average of payment will be different from the hypothesized value of $19.00. The results also show that the mean average price is $19.23 which is not significantly different from $19.00. 2. Randomization Condition which states that random sampling was used to select the respondents from the larger population. The 400 respondents were randomly drawn from the city’s population of 500,000. 3. Nearly Normal Condition or normality assumption: this condition is satisfied since the skewness value is -0.085 so it is very small. Also the histograms below show unimodal symmetric distribution for the sample 9.2 Hypothesis 2: Average income is not different from $70,000 Almost the assumptions and conditions of this test are satisfied: 1. Independent Assumption: we have no reason to check if the data values influence with the hypothesized value ($70,000). Also the boxplots indicate several outliers in the group, but no reason to delete them and their impact is minimal. 2. Randomization Condition: the people who were surveyed were selected at random. 3. 10% Condition: the population is 500,000 and the surveyed people are 400, so this condition is not met as this represents 0.08 percent of the total population. 4. Normal Population Assumption: the boxplots and histograms show unimodal and fairly symmetric distribution of the group surveyed. The boxplots and histogram show the distribution of the people surveyed about the mean of income per year. It look like the distribution for the group is unimodal and fairly symmetric. 9.3 Hypothesis 3: Elegant décor is preferred to simple décor. The independent samples t-Test was appropriate under the following assumptions and conditions: 1. Paired Data Assumption: The data are paired because they are ask the same group about the preference between (simple décor , elegant decor). 2. Randomization Condition: the people who were asked about the preference were selected at random. 3. Independent Assumption: the difference of preference is individual from any other in the group. 9.4 Hypothesis 4: Expenditure is different across marital groups The following assumptions and condition are checked for this test and they are satisfied: 1. Independence Assumption: the data for each group are collected independently from other group and there is no reason to influence the spending behavior between the groups. Also the sample was selected at random. 2. Equal variance assumption: the F-test is used to determine if the variances form the sample mean is difference across the particular groups. (F=99.939, p= 0.000). The results show that the variances in expenditure between the groups are significant since p=0.000 Read More