Differences in Tested Variables - Assignment Example

Data Analysis Report Name Number Course Tutor Date Data Analysis Report In this research study, several hypotheses were formulated based on the respective research questions. Appropriate tests were used to analyze and measure the differences in the tested variables. For all the statistical analyses, the alpha level of significance is set at .05. Results Question 1: To test whether the average amount that the people are willing to pay for each meal is less than the forecasted value of $ 19, formulate the null hypothesis (hypothesis 1) and test it against an alternative hypothesis. Hypothesis 1: The null hypothesis stated that the average amount that the people are willing to pay for each meal is equal to the forecasted value of $ 19, while the alternative hypothesis stated that the average amount that the people are willing to pay for each meal is less than the forecasted value of $ 19. For the sample selected, the average amount that the people are willing to pay for each meal (M = $19.23, SD = 7.56) is greater than the hypothesized value. The result of one sample t-Test revealed a non-significant difference, t (399) = .609, p = .272, at the alpha level of significance .05. Thus, fail to reject the null hypothesis. Therefore, the average amount that the people are willing to pay for each meal is not less than the forecasted value of $ 19. Question 2: To test whether the average income of the people surveyed differs from the hypothesized value of $70,000, formulate a null hypothesis (hypothesis 2) and test it against an alternative hypothesis. Hypothesis 2: The null hypothesis stated that the average income of the people that were surveyed is equal to $70,000, while the alternative hypothesis stated that the average income of the people that were surveyed differs significantly from $70,000. The sample survey average income (M = $77,087.50, SD = 28,896.93) is greater than the hypothesized value. The result of one sample t-Test revealed a significant difference, t (399) = 4.905, p < .001. At the alpha significance level of significance .05, reject the null hypothesis. Hence, the average income of the people that were surveyed is much greater than the estimated value of $70,000. Question 3: To test whether there is a difference between the preference for simple décor and elegant décor, formulate a null hypothesis (hypothesis 3) and test it against an alternative hypothesis. Hypothesis 3: The null hypothesis stated that the preference for simple décor and elegant décor are not related, while the alternative hypothesis stated that the preference for simple décor and elegant décor are related. The frequency statistics for the two variables are as illustrated in frequency tables below; Table 1: Frequency statistics (prefer 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 Table 2: Frequency statistics (Prefer 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 The cross tabulation analysis revealed a significant difference in the preference for simple décor and elegant decor, gamma = 1.000, p = .000. At the alpha significance level of .05; the null hypothesis should be rejected. Therefore, the preference for simple décor and elegant décor differ significantly. As indicated in the table 1 and 2 above, most of the people survey (28%) very strongly prefer elegant décor compared to only 6.3% who strongly prefer simple décor. Question 4: To evaluate whether there is a difference in the mean amount spent in restaurant every month among the different marital status, formulate a null hypothesis (hypothesis 4) and test it against an alternative hypothesis. Hypothesis 4: The null hypothesis stated that there is no difference in the mean amount spent in restaurant every month across the different marital status, while the alternative hypothesis stated that there is a difference in the meant amount spent in restaurant every month across the different marital status. The descriptive statistics of the mean amount spent in restaurant every month for the different marital status is as illustrated in table 3; Table 3: Descriptive Statistics How many total dollars do you spend per month in restaurants (for your meals only)? N Mean Std. Deviation Std. Error Minimum Maximum Single 146 $180.8904 $30.42280 $2.51781 $101.00 $240.00 Married 175 $232.6114 $29.87614 $2.25842 $174.00 $301.00 Other (Divorced, Widow, etc.) 79 $203.2785 $42.00792 $4.72626 $117.00 $307.00 Total 400 $207.9400 $40.11945 $2.00597 $101.00 $307.00 Analysis of Variance (ANOVA) showed that there was a significant difference in the mean amount spent in restaurant each month among the different marital status, F = 99.939, p = .000. Therefore, at the alpha significance level of .05; the null hypothesis is rejected. As indicated in table 3, the married people on average spend the most per month in restaurants compared to the people from the other marital status groups. Question 5: To test whether there is a difference between the mean preference for jazz combo and string quartet, formulate a null hypothesis (hypothesis 5) and test it against an alternative hypothesis. Hypothesis 5: The null hypothesis stated that there is no difference between the mean preference for jazz combo and string quartet, while the alternative hypothesis stated that there is difference between the mean preference for jazz combo and string quartet. The frequency statistics for the two variables are as illustrated in table 4 and 5 below; Table 4: Frequency statistics (prefer string quartet) 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 Table 5: Frequency statistics (prefer 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 7.3 7.3 91.0 Very Strongly Prefer 36 9.0 9.0 100.0 Total 400 100.0 100.0 The cross tabulation analysis revealed a significant difference in the preference for Jazz Combo and String Quartet, gamma = 1.000, p = .000. At the alpha significance level of .05; reject the null hypothesis. As indicated in the table 4 and 5 above, most of the people surveyed (16.3%) very strongly prefer String Quartet compared to only 9.0% who strongly prefer Jazz Combo. Question 6: To test whether there is an association between the likelihood of attending and which section of the newspaper is read, formulate a null hypothesis (hypothesis 6) and test it against an alternative hypothesis. Hypothesis 6: The null hypothesis stated that there is no association between the likelihood of attending and which section of the newspaper is read, while the alternative hypothesis stated that there is an association between the likelihood of attending and which section of the newspaper is read. The frequency statistics for the section of the news paper read are as illustrated in table 6 below; Table 6: Frequency statistics of the section of the newspaper 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 The cross tabulation analysis indicated that there was no association between the likelihood of attending and which section of the newspaper is read. The symmetric measure Cramer’s V= .102, p = .413, thus, at the alpha significance level of .05, fail to reject the null hypothesis. However, based on the frequency statistics in table 6 of the section of the newspaper read, most of people surveyed (28.0%) frequently read the business section of the newspaper. Question 7: To evaluate whether there is a difference in the average price that the people are willing to pay for each meal across the post codes, formulate a null hypothesis (hypothesis 7) and test it against an alternative hypothesis. Hypothesis 7: The null hypothesis stated that there is no difference in the average price that the people are willing to pay for each meal across the post codes, while the alternative hypothesis stated that there is a difference in the average price that the people are willing to pay for each meal across the post codes. The descriptive statistics of the average price that the people are willing to pay for each meal across the post codes are as illustrated in table 7; Table 7: Descriptive Statistics What would you expect an average evening meal to be priced? N Mean Std. Deviation Std. Error Minimum Maximum A (1 & 2) 93 $19.4409 $8.09114 $0.83901 $1.00 $39.00 B (3, 4, & 5) 109 $20.7523 $7.16881 $0.68665 $1.00 $38.00 C (6, 7, 8, & 9) 94 $17.5745 $8.39417 $0.86579 $1.00 $35.00 D (10, 11, & 12) 104 $18.9423 $6.34880 $0.62255 $1.00 $36.00 Total 400 $19.2300 $7.55943 $0.37797 $1.00 $39.00 Analysis of Variance (ANOVA) showed that there was a significant difference in the average price that the people are willing to pay for each meal across the post codes, F = 3.099, p = .027. Therefore, at the alpha significance level of .05; the null hypothesis is rejected. Table 7, with the descriptive statistics indicates that people with post codes B (3, 4, & 5) have the highest mean price expectation of an average meal at the restaurant. Question 8: To test whether there is a difference in the average monthly restaurant expenditure across the genders, formulate a null hypothesis (hypothesis 8) and test it against an alternative hypothesis. Hypothesis 8: The null hypothesis stated that there is no difference in the average monthly restaurant expenditure across the genders, while the alternative hypothesis stated that there is a difference in the average monthly restaurant expenditure across the genders. The descriptive statistics of the average monthly restaurant expenditure across the genders are as illustrated in table 8 below; Table 8: Descriptive statistics What is your gender? N Mean Std. Deviation Std. Error Mean How many total dollars do you spend per month in restaurants (for your meals only)? Male 204 $202.1569 $42.77268 $2.99469 Female 196 $213.9592 $36.29690 $2.59264 The independent samples t-Test; Levene’s test for equality of variance showed that the variances were unequal, F = 6.711, p = .010. The t-Test for equality of means revealed a significant mean difference, t (398) = -2.97, p = .003, at the alpha significant level of .05. Therefore, reject the null hypothesis. Table 8, with the descriptive statistics indicates that females spend more on average per month in restaurants than the males. Question 9: To evaluate whether there is a relationship between income and total expenditure, formulate a null hypothesis (hypothesis 9) and test it against an alternative hypothesis. Hypothesis 9: The null hypothesis stated that there was no relationship between income and total expenditure, while the alternative hypothesis stated that there is a relationship between income and total expenditure. The assumptions of normality were checked; it appeared the data were normally distributed, ratio scale. The correlation statistics are indicated in table 9 below; Table 9: Correlation Statistics What is your annual salary? How many total dollars do you spend per month in restaurants (for your meals only)? Pearson Correlation .134** Sig. (2-tailed) .007 N 400 Scatter plot of income against total expenditure Graph 1 The correlation analysis indicates that there is a significant positive relationship between income and total expenditure. Therefore, at the alpha significant level of .05, reject the null hypothesis. This implies that the total expenditure tends to increase with increase in income. Question 10: To evaluate whether the average amount that people spend on food every month can be explained by the average price that the people are willing to pay for their meals, age, marital status, gender and income, formulate a null hypothesis (hypothesis 10) and test it against an alternative hypothesis. Hypothesis 10: The null hypothesis for regression stated that there was no relationship between the average amount that people spend on food every month and the independent variables (average price that the people are willing to pay for their meals, age, marital status, gender and income), while the alternative hypothesis stated that there is a relationship between the average amount that people spend on food every month and the independent variables (average price that the people are willing to pay for their meals, age, marital status, gender and income). The assumptions of normality were checked; it appeared the data variables were normally distributed, ratio scale. The regression analysis summary is as illustrated in the tables below; Table 10: Regression coefficient estimates Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 124.762 11.968 10.425 .000 What would you expect an average evening meal to be priced? .037 .246 .007 .149 .882 Age .795 .214 .176 3.718 .000 What is your marital status? 14.553 2.593 .266 5.613 .000 What is your gender? 9.059 3.753 .113 2.414 .016 What is your annual salary? .000 .000 .116 2.487 .013 a. Dependent Variable: How many total dollars do you spend per month in restaurants (for your meals only)? Analysis of Variance (ANOVA) showed that there was a significant relationship between the dependent variable and the independent variables, F = 14.480, p = .000. Therefore, at the alpha significance level of .05; the null hypothesis is rejected. Thus, the independent variables (average price that the people are willing to pay for their meals, age, marital status, gender and income) can be used to estimate the average amount that people spend on food each month. Recommendations Based on the results of the survey, the people in post codes B (3, 4, & 5) are willing to spend the most in restaurants, hence the best location for Michael Jenkins’ restaurant would be within the post codes B (3, 4, & 5). In addition, the average amount that the people are willing to pay for each meal is not less than the forecasted value of $ 19. Therefore, when pricing the meals sold at the restaurant, the management can use the $19 price as the base price. Most of the people surveyed (28%) very strongly prefer elegant décor compared to only 6.3% who strongly prefer simple décor. Therefore, Michael should consider using elegant décor in his restaurant. The market research results showed that the females and married people on average spend the most per month in restaurants compared to males and the people from the other marital status groups. Therefore, during marketing, the team marketing the restaurant should try to target the married people and females more. However, the other groups of people should also as well be targeted during marketing campaigns. The most convenient section of the newspaper to market the restaurant would be the business section. This is because most people prefer reading the business section of the newspaper. Furthermore, most of the people surveyed prefer string quartet. Therefore, Michael should plan to have String quartet play in the restaurant most of the time so as to attract more customers to his restaurant. References Green, S. B. (2008). Using SPSS for Window and Macintosh: Analyzing and Understanding data (5th ed.), Upper Saddle River, NJ: Pearson Prentice Hall. Read More