Question

You and some of your friends have decided to test the validity of an advertisement by a local pizza restaurant, which claims it delivers to the dormitories faster than a local branch operated by a national chain. Both the local pizza restaurant and the national chain are located across the street from your college campus. The variable of interest is delivery time in minutes from the time the pizza is ordered to when it is delivered. You collect the data ordering 16 pizzas from local pizza restaurant and 16 from the national chain at different times. The following table is the record of the delivery times: At the .05 level of significance, is there any evidence that the mean delivery time the local pizza restaurant in less than the mean delivery time for the national chain? Local (Delivery time in minutes) National Chain (Delivery time in minutes) 16.8 18.1 15.6 16.7 17.5 18.2 19.2 13.7 11.7 14.1 21.8 13.9 20.8 21.5 12.2 11.4 22.0 15.2 18.7 15.6 20.8 19.7 21.2 23.9 19.5 17.0 19.5 16.5 24.0 23.0 16.7 17.5 Complete testing in Minitab and prepare report in Word. Enter the data presented above into a Minitab worksheet. Conduct the test with alpha of .05 and complete the following. Using the six step process for each hypothesis test complete the following for the Pizza Delivery analysis • Set up the six-step process and using an f test determine if the data has equal variances. Include only the critical value and p value techniques in your conclusion. Present the Minitab output in your conclusion. For your interpretation discuss whether the distributions have equal variances. Do not include graphs from the F test. • Set In your conclusion present the output from Minitab for: o Critical value/critical ratio technique o pvalue o Confidence intervals. • Based on the characteristics of each of the above techniques include statements regarding Fail to reject or rejection of the null and type of error which may have been made. • Interpretation: State whether the variances are significantly different and which type of T test you will undertake given the outcome of the f test you just completed. • Use boxplot to satisfy assumption of normality as sample size is <30. Provide a brief description with the graph as to how normality is or is not supported.

Answer 1

1. Here, we perform two sample t test to test mean delivery time of local pizzas and national chain pizzas
   We want to test,
   : Mean delivery time of local pizzas and national chain pizzas is same
   Vs : Mean delivery time of local pizzas is less than national chain pizzas
   i.e. $wwF7vjf1pg3aR9kGgwAAAABJRU5ErkJggg==$ Vs
   We perform test in minitab as Stat>Basic Statistics>2-Sample t test

Two-Sample T-Test and CI: Local, National

Two-sample T for Local vs National

           N      Mean     StDev   SE Mean

Local     16     16.45      3.41      0.85

National 16     19.38      2.86      0.71

Difference = mu Local - mu National

Estimate for difference: -2.93

95% upper bound for difference: -1.04

T-Test of difference = 0 (vs <): T-Value = -2.64 P-Value = 0.007 DF = 29

Decision: Here, P-Value = 0.007 < level of significance 0.05

There is enough evidence to reject .

Conclusion: We may conclude that mean delivery time of local pizzas is less than national chain pizzas

1. Here, we perform f test to test variation in delivery time for local pizzas and national chain pizzas
   We want to test,
   : Variation between delivery time of local pizzas and national chain pizzas is same
   Vs : Variation between delivery time of local pizzas and national chain pizzas is not same
   i.e. $A0w8ivbYgAAAABJRU5ErkJggg==$ Vs $9jg5Sw+CqzwAAAABJRU5ErkJggg==$
   We perform test in minitab as Stat>Basic Statistics>2-variances

Test for Equal Variances

Level1     Local

Level2     National

ConfLvl    95.0000

Bonferroni confidence intervals for standard deviations

  Lower     Sigma     Upper     N Factor Levels

2.41547   3.40705   5.64873    16 Local  

2.02666   2.85862   4.73946    16 National

F-Test (normal distribution)

Test Statistic: 1.421

P-Value       : 0.505

Levene's Test (any continuous distribution)

Test Statistic: 0.654

P-Value       : 0.425

Decision: Here, P-Value = 0.425> level of significance 0.05

We fail to reject .

Conclusion: We may conclude that variation between delivery time of local pizzas and national chain pizzas is same