## Answers

- 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. 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

- 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. Vs

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

.