Problem 2: A regional manager want to know if there is a difference between the

Question

Problem 2:

A regional manager want to know if there is a difference between the mean amounts of time that customers wait in line at the drive-through window for the three stores in her region. She samples the wait times at each store. Her data are given in the following table. Use an ANOVA test to determine if there is a difference between the mean wait times for the three stores, at the 0.05 level of significance.

Drive-Through Wait Times (in Minutes)

Store 1

Store 2

Store 3

Step 1. (4 pts) State the null and alternate hypothesis.

2

Step 2. (6 pts) Fill in the ANOVA table.

SS

df

MS

F

Treatments

Error

XXXXXXXXXXX

Total

XXXXXXXXXXXX

XXXXXXXXXXX

Step 3. (2pts) Find the value of the test statistic. (Round your answer to 3 decimals)

Step 4. (2 pts) Find the degrees of freedom associated with the test statistic for this problem.

Step 5. (2 pts) Find the critical value of the test statistic. ( Round your answer to 3 decimals )

Step 6 (2 pts)At the 0.05 level of confidence, determine whether to fail to reject or reject the null hypothesis.

Step 7 (2 pts)What is the conclusion at the 0.05 level of significance?

Store 1

Store 2

Store 3

2.34 2.87 1.32 1.23 1.94 1.45 1.89 2.36 1.78 2.31 1.85 2.01 3.02 1.75 2.45 1.95 2.82 1.92 2.45 3.32 1.83

Explanation / Answer

1) null hypothesis::  mean wait times for the three stores are same

alternate hypothesis: there is a diffiernce in mean wait time for at least 2 stores

2)

3) f statistic:2.295

4) degree of freedom with test stat are 2 in numerator and 18 in denomiantor

5)critical value =3.554

6) we fail to reject null hypothesis.

7) we do not have sufficienmt evidence to conclude that   there is a difference between the mean wait times for the three stores

Groups Count Sum Average Variance Store 1 7 15.19 2.17 0.309967 Store 2 7 16.91 2.415714 0.363362 Store 3 7 12.76 1.822857 0.13859 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1.242181 2 0.62109 2.294898 0.129492 3.554557 Within Groups 4.871514 18 0.27064 Total 6.113695 20

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