Wait time for customers at the MacHamburger Shack has been in increasing issue f
ID: 3155021 • Letter: W
Question
Wait time for customers at the MacHamburger Shack has been in increasing issue for you and your employees. Ideally, you, as the manager, would like to have the wait time to be no more than 2 minutes per customer, once the order has been processed. In an effort to understand how long a customer must currently wait after the order is processed, you implement a process of timing each transaction. You collect the following data (in minutes):
WaitTime
1.6 5.8
6.6 3.4
5.6 9.3
5.1 7.4
3.9 1.8
4.6 6.2
6.5 5.4
6.4 4.9
8.6 5.4
4.2 0.8
Conduct an appropriate test, where you do not know the industry standard deviation for wait time. You would like your wait time to be 2 minutes (with 95% confidence), but do not know if your actual time is more or less than 2 minutes. After you conduct the test answer the following questions.
Step 1 of 6: The standard error of the mean is (rounded to 3 decimals):
Step 2 of 6: The 95% Confidence Interval for the mean (round to 3 decimals):
Step 3 of 6: The p-value for the test is:
Step 4 of 6: The true (population) mean is between:
Step 5 of 6: Based on the p-value and the 95% confidence interval:
Explanation / Answer
Given n = 20
X
(x-X)2
1.6
12.7806
6.6
2.0306
5.6
0.1806
5.1
0.0056
3.9
1.6256
4.6
0.3306
6.5
1.7556
6.4
1.5006
8.6
11.7306
4.2
0.9506
5.8
0.3906
3.4
3.1506
9.3
17.0156
7.4
4.9506
1.8
11.3906
6.2
1.0506
5.4
0.0506
4.9
0.0756
5.4
0.0506
0.8
19.1406
The null hypothesis is
Against the alternative hypothesis
Test statistic
T= x - µ /S2/n
=5.1750 -2 / 31.3740/20
= 2.5349
The slandered error is S/sqrt(n) = 1.2525
95% confidence interval x ±t0.05 S/sqrt(n) = [2.5535,7.7965]
P value is <0.00001
The result is significant at p<0.05
X
(x-X)2
1.6
12.7806
6.6
2.0306
5.6
0.1806
5.1
0.0056
3.9
1.6256
4.6
0.3306
6.5
1.7556
6.4
1.5006
8.6
11.7306
4.2
0.9506
5.8
0.3906
3.4
3.1506
9.3
17.0156
7.4
4.9506
1.8
11.3906
6.2
1.0506
5.4
0.0506
4.9
0.0756
5.4
0.0506
0.8
19.1406
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