Data Analysis for Heavenly Chic Restaurant - Statistics Project Example

Data analysis report: Heavenly Chic- A restaurant Supervisor: October 15, Data analysis report: Heavenly Chic-A restaurant Introduction Statistics plays an important role in business decision making. Test of hypothesis, for example, ascertains significance of observations to eliminate probability of chance and establishes confidence in decisions. It applies statistical tools such as analysis of variance and statistical distributions to evaluate trends in data and their associated differences. This paper applied test of hypothesis to analyze data on Michael Jenkins’ proposed business. Background information Michael Jenkins, a restaurant-supply sales representative, has a dream of establishing an upscale restaurant. He has worked in a large metropolitan and interacted with many restaurant owners. He has also reviewed his capital based and ascertained potential to finance this dream commercial venture. He is however uncertain of the potential market and taste and preferences among people in his target location. Some of the major concerns that Michael has discussed with a research company relate to existence of demand for an upscale restaurant the price level, design and operational characteristics, suitable location, and possible strategies for promoting the business. Data is available of factors to the business based on the city’s demographics and this paper analyzes the data for an informed position regarding feasibility of the proposed business venture. The data analysis focuses on the following issues. Amount of money that potential patrons are willing to pay for entrees, and if $ 18 is a correct forecast for the amount Possibility that all patrons will spend about $ 200 per month on food Suitability of location by post code Variation of potential patrons’ average monthly expenditure by their incomes Necessity of waterfront views and possibility that patrons will drive for less than 30 minutes to the restaurant Relevance of unusual desserts and unusual entrees to patrons Sections of the newspaper for promoting the business venture Significance of age, family size and gender on restaurant preference Significance of difference in family size between probable and non-probable patrons Relationship between marital status and probability that one would be a patron Results and discussion Amount that patrons are willing to pay The average amount that patrons are willing to pay is $ 165.86. This appears to be well above the forecasted $ 18 and suggest that the forecast is a correct minimum limit. The following table shows descriptive statistics for average amount that can be spent in the restaurant. Table 1: Average price Descriptive Statistics N Minimum Maximum Mean Std. Deviation avprice 400 6.00 999.00 165.8600 350.54418 Valid N (listwise) 400 Test of hypothesis is however, necessary to ascertain validity of the forecast and the following is the set of hypothesis for evaluation. HO: µAvexp=18, Average expenditure is not greater than 18, forecast is not correct HA: µAvexp>18, Average expenditure is greater than 18, forecast is correct One sample t test that compares mean of a distribution with a hypothesized mean is used to analyze the data and the following SPSS output summarizes the results. Table 2: Results for one sample test on average expenditure in the restaurant One-Sample Test Test Value = 18 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper avprice 8.436 399 .000 147.86000 113.4028 182.3172 The results show a significant t-test because of the low p-value, 0.00, relative to test’s level of significance, 0.05. t-statistic is 8.436. This means that the null hypothesis is rejected to the effect. The average expenditure is therefore greater than $ 18 and the estimate is correct. Patron’s average monthly expenditure The following set of hypothesis is used to determine whether Michael can anticipate all patrons to spend an average of $ 200 per month on food. HO: µAvetotspe=200, All patrons are likely to spent an average of $ 200 dollars a month on food HA: µAvetotspe≠ 200, All patrons are not likely to spent an average of $ 200 dollars a month on food The one sample student t test is suitable for the analysis that compares mean of a single sample to a hypothesized mean. This is a two-tailed test and the following are the results at 0.05 level of significance. Table 3: Results for average total monthly expenditure among patrons One-Sample Test Test Value = 200 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper totspent -10.775 399 .000 -49.94750 -59.0602 -40.8348 Results indicate a significant test, p-value=0.00, t=-10.775. This means that the null hypothesis is rejected to the effect that the average amount to be spent by patrons per month is not equal to $ 200. This means that some of the patrons will not spend $ 200 per month in the restaurant. Likelihood of attendance to the proposed restaurant by postcode Frequency based on postcodes explains distribution of potential attendants by code. The following table summarises the statistics. Table 4: Distribution by postal code postcode Frequency Percent Valid Percent Cumulative Percent Valid 1.00 20 5.0 5.0 5.0 2.00 120 30.0 30.0 35.0 3.00 220 55.0 55.0 90.0 4.00 40 10.0 10.0 100.0 Total 400 100.0 100.0 The table identifies postal code 3 as the best location for the proposed venture. Analysis of variance that evaluates association between variables is suitable for analyzing possible differences in likelihood of attendance across postal code based on the following hypotheses. HO: µ1= µ2= µ3 = µ4, no significant difference in likelihood of attendance across the postal codes HA: anything different, Likelihood of attendance differs across the postal codes Table 5: Analysis of variance for difference of likelihood of attendance across postal codes ANOVA likely Sum of Squares df Mean Square F Sig. Between Groups 370.710 3 123.570 203.647 .000 Within Groups 240.287 396 .607 Total 610.998 399 The low p-vale, p=0.000, F= 203.647, shows that the ANOVA test is significant. This means that the null hypothesis is rejected to the effect that mean likelihood of attendance is not equal across postal codes. Attendance in some areas is therefore likely to be higher than in other areas and areas under code 3 promises higher likelihood. Michael should therefore consider code 3 for the start up in the city. Average monthly expenditure by patron’s income The following set of hypothesis is explored for significance of difference average monthly expenditure by patrons’ income. HO: µ1= µ2= µ3 = µ4= µ5= µ6= µ7, no significant difference in average monthly expenditure by patron’s income levels HA: anything different, Patron’s average monthly expenditures differ by income level One-way analysis of variance is the appropriate test for the hypothesis because of its scope that explores difference in variable averages by groups and organization income levels into ordinal quantity. The following is the SPSS output for the analysis results. Table 6: ANOVA table for variation of average monthly expenditure by income level ANOVA totspent Sum of Squares df Mean Square F Sig. Between Groups 2872939.899 6 478823.317 338.298 .000 Within Groups 556247.998 393 1415.389 Total 3429187.898 399 The results identify significance of the F test based on the low p-value, 0.000, F=338.289. This means that the null hypothesis is rejected to mean that the patrons’ monthly expenditures depend on their income levels. Income should therefore be a significant factor to determining location. Need for waterfront views and drive duration Distribution of drive period identifies the following frequencies. Table 7: Frequency distribution for drive duration drive Frequency Percent Valid Percent Cumulative Percent Valid 1.00 72 18.0 18.0 18.0 2.00 141 35.3 35.3 53.3 3.00 68 17.0 17.0 70.3 4.00 63 15.8 15.8 86.0 5.00 56 14.0 14.0 100.0 Total 400 100.0 100.0 A majority of the patrons, 70 percent, will drive for at most thirty minutes and this undermines the need for waterfront views. Significance of difference between desserts to patrons The likelihood of attendance based on choice of dessert offers a basis for determining patrons’ preference for types of dessert. The following set of hypothesis is used. HO: µ1= µ2= µ3 = µ4= µ5, no significant difference in average in preference based on type dessert HA: anything different, Patron’s likelihood of attendance depends on type of dessert Analysis of variance’s F test is the most appropriate for determining significance of variation in preference across the non-numeric dessert scale. Bellow is the test results Table 8: Preference based on dessert ANOVA likely Sum of Squares df Mean Square F Sig. Between Groups 350.730 4 87.683 133.073 .000 Within Groups 260.267 395 .659 Total 610.998 399 The test is significant because of the low p-value, 0.000, F=133.073. The null hypothesis is rejected because of the small p value to the effect that patrons prefer one dessert type than others. Descriptive statistics based on the following frequency distribution shows that patrons prefer dessert 1. Suitable section of the newspaper for advertisement Distribution of patron’s preference for section of the newspaper and significance of the section of newspaper read on likelihood of attendance is important to selection of the section of the newspaper for advertisement. The following hypotheses are used to establish significance of read newspaper section on the patrons’ likelihood of visiting the restaurant. HO: µ1= µ2= µ3 = µ4= µ5= µ99, no significant difference in likelihood of attendance based on section of newspaper read HA: anything different, section of newspaper read is significant in determining likelihood of a patron’s attendance. Analysis of variance is the suitable tool because of its property to evaluate differences across groups. Table 9: Significance of newspaper sections ANOVA likely Sum of Squares df Mean Square F Sig. Between Groups 244.006 5 48.801 52.393 .000 Within Groups 366.992 394 .931 Total 610.998 399 The results identify significance of the F test, p=0.000. The null hypothesis is rejected to the effect that section of newspaper is significant to patrons’ preference. The most moular section should therefore be used for advertisement. The following table shows frequency distribution for popularity of sections of newspaper. Table 10: Frequency distribution across newspaper sections secpaper Frequency Percent Valid Percent Cumulative Percent Valid 1.00 52 13.0 13.0 13.0 2.00 65 16.3 16.3 29.3 3.00 118 29.5 29.5 58.8 4.00 57 14.3 14.3 73.0 5.00 87 21.8 21.8 94.8 99.00 21 5.3 5.3 100.0 Total 400 100.0 100.0 The section under code three is therefore the most suitable for advertising. Total monthly spent by age, family size, and gender Relationship between total monthly expenditure and age, family size, and gender can be explored through the following set of hypothesis. H0: βi=0, for any i, there is no significant relationship between age, family size, and gender and total monthly expenditure in the restaurant. HA: βi≠ 0, for any i, variable i is significant in explaining total monthly expenditure. Regression analysis is suitable for the analysis because of its feature that develops a model for relationship between quantitative variables. The following is the result for the analysis. Table 11: ANOVA table for total monthly spent by age, family size, and gender ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 666048.623 3 222016.208 31.818 .000b Residual 2763139.275 396 6977.624 Total 3429187.897 399 a. Dependent Variable: totspent b. Predictors: (Constant), famsize, gender, age The test is significant because of the small p-value, 0.000 that leads to rejection of the nuss hypothesis and the conclusion that age, gender, and family size influences total amount spent in the restaurant per month. The following tables determine significance of each of the factors. Table 12: Table of coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -59.401 28.668 -2.072 .039 gender -6.699 8.361 -.036 -.801 .423 age 4.223 .440 .433 9.602 .000 famsize -5.781 3.102 -.084 -1.864 .063 a. Dependent Variable: totspent The test is only significant for age and this means that gender and family size does not dictate the total amount spent by a patron Difference in family size across probable and non-probable patrons The following hypothesis set is used to determine significance of variation in family size across the probable and non-probable patrons. HO: µp= µup, no significant difference in family size by probability HA: µp≠ µup anything different, Patron’s average monthly expenditures differ by income level Analysis of variance for difference between groups is suitable evaluating the hypotheses. The following table summarizes the results. Table 13: ANOVA table for family size across probable and non-probable patrons ANOVA famsize Sum of Squares df Mean Square F Sig. Between Groups 5.877 1 5.877 3.243 .072 Within Groups 721.283 398 1.812 Total 727.160 399 The test is not significant because of the high p-vale, 0.072, F=3.243. This means that the null hypothesis is not rejected no significant difference exist in family size between probable and non probable patrons. It shows that family size is the same regardless of probability of the patrons. Differences in marital status across probable and non-probable patrons The following set of hypotheses evaluates the difference. HO: µp= µup, no significant difference in family size by probability HA: µp≠ µup anything different, Patron’s average monthly expenditures differ by income level One-way ANOVA is suitable because of its potential to evaluate differences across group frequencies. The following table summarizes the results Table 14: ANOVA table for marital status across probable and non-probable patrons ANOVA marital Sum of Squares df Mean Square F Sig. Between Groups .015 1 .015 .050 .824 Within Groups 119.575 398 .300 Total 119.590 399 The test is not significant because of the high p-value, F=0.50. The null hypothesis is not rejected to the effect that no significant difference in marital status occurs between probable and non-probable patrons. The patrons therefore demonstrate similar distribution in marital status. Conclusion Patrons are willing to pay more than $ 18 for entrée but their average expenditure is not $ 200. Postal code, patrons’ income, dessert, section of newspaper that patrons read, and age are significant to feasibility of the proposed restaurant and should be reviewed in determining a suitable location for a start up. Read More