Question

Please, help with this question

11.11 QSR has been reporting on the largest quick-serve and fast-casual brands in the United States. The file FastFoodChain contains the food segment (burger, chicken, pizza, or sandwich) and U.S. mean sales per unit ($ thousands) for each of 37 quick-service brands.

1. At the 0.05 level of significance, is there a difference in the mean U.S. mean sales per unit ($ thousands) among food segments?
2. At the 0.05 level of significance, is there a difference in the variation in U.S. average sales per unit ($ thousands) among food segments?

Burger	Chicken	Sandwich	Pizza/Pasta
2400.0	933.0	452.0	855.0
1230.0	2694.4	2200.0	657.0
1418.0	1053.0	838.0	863.0
1023.0	695.0	420.0	460.0
1322.0	1548.0	753.0	538.5
540.0	1573.3	2226.6	908.0
1054.0	1400.0	988.0	623.0
1709.0	1015.0
1590.0
1139.0
1641.2
830.4
1300.0
1925.0
1036.0

Answer 1

Objective: To compare the average sales across the food segments namely, Burger, Chicken, Sandwich and Pizza

The appropriate statistical test to carry out the above objective would be a One-way ANOVA, with the following assumptions:

- The samples are independent - Errors/residuals are normally distributed - Homogeneity of Variance (To test: H₀: Valriances of all four groups are equal Vs H_a: Not all variances are equal)

Let $\mu_{1},\mu_{2},\mu_{3},\mu_{4}$ denote the population means of Sales belonging to the groups Burger, Chicken, Sandwich and Pizza

To test:$H_{0}:\mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}$ Vs $H_{a}:$ Not all means are equal

Using SPSS,

View Data Transform Analyze Direct Marketing Graphs Utilities Add-ons Window Help Reports Descriptive Statistics Tables Food_segment Value Compare Means M Means... 2400.00 Burge General Linear Model One-Sample T Test... Burge Burge Burge Burge Burge Burge Burge 1230.00 Generalized Linear Models Independent-Samples T Test... 1418.00 Mixed Models Paired-Samples T Test... 1023.00 Correlate One-Way ANOVA... 1322.00 Regression 540.00 Loglinear 1054.00 Neural Networks 1709.00 Classify 1590.00 Burge Dimension Reduction 4120 oo.

Food_segment Value var var var var var var var 2400.00 Burger One-Way ANOVA 1230.00 Burger Dependent List 1418.00 Burger Contrasts... 1023.00 Burger Value Post Hoc... 1322.00 Burger Options 540.00 Burger ... ..www. ... 1054.00 Burger Bootstrap. 1709.00 Burger 1590.00 Burger Factor 1139.00 Burger Food_segment 1641.20 Burger OK Paste Reset Cancel Help 830.40 Burger 1300.00 Burger 1025.00 D..rar

X One-Way ANOVA: Options Food_segment Value var va var var 2400.00 Burger Statistics 1230.00 Burger Descriptive Burger 1418.00 Contrasts... Fixed and random effects 1023.00 Burger Homogeneity of variance test Post Hoc... 1322.00 Burger Brown-Forsythe Options.. 540.00 Burger Welch 1054.00 Burger Bootstrap.. 1709.00 Burger Means plot 1590.00 Burger Missing Values 1139.00 Burger O Exclude cases analysis by analysis 1641.20 Burger Exclude cases listwise 830.40 Burger 1300.00 Burger Help Continue Cancel 1925.00 Burger 1036.00 Burger

We get the Output:

Descriptives Value 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Burger 15 1343.8400 462.12927 119.32126 1087.9213 1599.7587 540.00 2400.00 844,6705 2694,40 Chicken 1363.9625 621.14717 219.60869 1883.2545 695.00 291.08265 2226.60 Sandwich 7 1125.3714 770.13230 413.1178 1837.6250 420.00 Pizza 7 700.6429 175.74383 66.42492 538.1069 863.1788 460.00 908.00 93.86739 1375,5449 Total 37 1185.1730 570.97301 994.8011 420.00 2694.40 Test of Homogeneity of Variances Value Levene Statistic df1 df2 Sig 2.834 3 33 .053 ANOVA Value Sum of Mean Square Sig Squares df F Between Groups 2301773.547 767257,849 3 2.684 063 Within Groups 9434593.006 33 285896,758 Total 1.174E7 36 LL

The p-value of the test represents the probability of obtaining a result as extreme as the one obtained, when the null hypothesis is true; a p- value < alpha (significance level) would imply that the probability of H₀ being true is very low, which suggests that the null hypothesis might actually be false, leading to rejection of H₀ at alpha level of significance.

Test for Homogeneity of Variance:

Here, since, the p- value of the test p = 0.053 > 0.05, we fail to reject the null hypothesis. We may conclude that there is no difference in the variation in U.S. average sales per unit ($ thousands) among food segments .

Test for Equality of Means:

Here, since, the p- value of the test p = 0.063 > 0.05, we fail to reject the null hypothesis. We may conclude that there is no difference in the mean sales per unit ($ thousands) among food segments.

Using excel,

BOOKT MIcrosoft Excel Cin Data Home Insert Page Layout Formulas Review View EShow Detail Connections K Clear Data Analysis Properties Reapply Hide Detail From Filter Text to Data From From From Other Existing Connections Refresh Sort Remove Columns Duplicates Validation Consolidate What-If Group Ungroup Subtotal Advanced GEdit Links Text Analysis Access Web Sources All Data Tools Get External Data Connections Sort & Filter Outline Analysis fox K10 A В C F G Н K M N O P Q R. S T 1 Burger Chicken Sandwich Pizza/Pasta X Data Analysis 2 2400 933 452 855 Analysis Tools 2694,4 1230 2200 657 ОК Anova: Single Factor Anova: Two-Factor With Replication Anova: Two-Factor Without Replication Correlation Covariance Descriptive Statistics Exponential Smoothing F-Test Two-Sample for Variances Fourier Analysis Histogram 4 1053 1418 838 863 Cancel 420 5 1023 695 460 1322 6 1548 753 538.5 Help 7 540 1573.3 2226.6 908 1054 1400 988 623 1709 1015 10 1590 11 1139 12 1641.2 020 4. 13

A1 Anova: Single Factor А D E Input 1 Burger Chicken Sandwich Pizza/Pasta ОК SA$1:$D$16 855 657 863 Input Range: 2 2400 933 452 Cancel 3 2200 Grouped By: Columns 1230 2694.4 Rows 1418 Help 4 1053 838 Labels in first row 460 538.5 5 695 1023 420 Apha: 0.05 753 6 1322 1548 7 908 623 2226.6 540 1573.3 Output options 1054 1400 988 Qutput Range $F$2 9 1709 1015 10 11 12 13 14 New Worksheet Ply: 1590 New Workbook 1139 1641.2 830.4 1300 15 16 1925 1036 17 X

А В C F G Н К L Sandwich Pizza/Pasta Chicken Burger Anova: Single Factor 2400 933 452 855 1230 2694.4 2200 657 1418 1053 838 863 SUMMARY Average Variance 1023 695 420 460 Groups Count Sum 753 1322 1548 538.5 Burger 15 20157.6 1343.84 213563.5 Chicken 540 1573.3 2226.6 908 10911.7 1363.96 385823.8 Sandwich 7877,6 1054 1400 988 623 7 1125.37 593103.8 Pizza/Pasta 4904,5 1709 1015 7 700.64 30885.89 1590 1139 1641.2 ANOVA F crit Source of Variation df P-value 830.4 SS MS F Between Groups 2.89 1300 2301774 3 767257.8 2.68 0.06 Within Groups 1925 9434593 33 285896.8 1036 Total 11736367 36

Test for Equality of Means:

Here, since, the p- value of the test p = 0.063 > 0.05, we fail to reject the null hypothesis. We may conclude that there is no difference in the mean sales per unit ($ thousands) among food segments.