MBA – MS
Term 1 –fall 2017
Exercises October 17, 2017
Exercise 9.46 (a-d)
… The restaurant would like to test the hypothesis that the average delivery time is less than 30 minutes. The following data represent a random sample of delivery times:
23 24 23 36 30 40 34 24 28 29 15 27
Using α=0.10, answer the following
- State the null and the alternative hypothesis
- Does the sample provide enough evidence to support Season’s delivery system?
- Verify your results using PHStat2
- Report the p-value from PHStat2 and interpret to meaning.
Descriptive Statistics
Data | ||||
Sample Size | 12 | |||
Sample Mean | 27.75 | |||
Sample Standard Deviation | 6.743683914 | |||
Null Hypothesis: μ0=>30
We assume that the delivery waiting time is at least 30 minutes or equal to 30 minutes.
Alternative Hypothesis: μα<30 min
We assume that the delivery time is less than 30 minutes.
We use t-student to test the hypothesis
t Test for Hypothesis of the Mean | ||||
Data | ||||
Null Hypothesis μ= | 30 | |||
Level of Significance | 0.1 | |||
Sample Size | 12 | |||
Sample Mean | 27.75 | |||
Sample Standard Deviation | 6.743683914 | |||
Intermediate Calculations | ||||
Standard Error of the Mean | 1.9467 | |||
Degrees of Freedom | 11 | |||
t Test Statistic | -1.1558 | |||
Lower-Tail Test |
| Calculations Area | ||
Lower Critical Value | -1.3634 | For one-tailed tests: | ||
p-Value | 0.1361 | T.DIST.RT value | 0.136128674 | |
Do not reject the null hypothesis |
| 1-T.DIST.RT value | 0.863871326 |
As p-value is 0.1361 and α=0.1 we do not reject the null hypothesis. That means the sample does not provide enough evidence that Season’s restaurant delivery system have a waiting time less than 30 minutes.
Probably clients are right and they have to wait more than Seasons claimed for delivery provide.
Exercise 9.47
Data | |
Sample Size | 20 |
Sample Mean | 56.45 |
Sample Standard Deviation | 6.125657859 |
Descriptive statistics
Null Hypothesis: μ0<=59.3 (Assuming resident doctors of the particular hospital are working less than 59.3 hours or exactly 59.3 hours per week)