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# Test of hypothesis for dependent samples

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Blockbuster is testing a new policy of waiving all late fees on DVD rentals using a sample of 10 randomly chosen customers.
(a) At alpha= .10, does the data show that the mean number of monthly rentals has increased?
(b) Is the decision close ?
(c) Are you convinced?

DVDRental

Customer No Late fee Late fee
1 14 10
2 12 7
3 14 10
4 13 13
5 10 9
6 13 14
7 12 12
8 10 7
9 13 13
10 13 9

https://brainmass.com/statistics/hypothesis-testing/test-of-hypothesis-for-dependent-samples-222337

#### Solution Preview

Blockbuster is testing a new policy of waiving all late fees on DVD rentals using a sample of 10 randomly chosen customers.
(a) At alpha (a) = .10, does the data show that the mean number of monthly rentals has increased?
(b) Is the decision close ?
(c) Are you convinced?

Customer No Late fee Late fee
1 14 10
2 12 7
3 14 10
4 13 13
5 10 9
6 13 14
7 12 12
8 10 7
9 13 13
10 13 9

(a) At alpha (a) = .10, does the data show that the mean number of monthly rentals has increased?

First we calculate the mean and standard deviation of difference
Customer No Late fee Late fee "Difference
"
1 14 10 4
2 12 7 5
3 14 10 4
4 13 13 0
5 10 9 1
6 13 14 -1
7 12 12 0
8 10 7 3
9 13 13 0
10 13 9 4

Calculation of Mean ...

#### Solution Summary

Uses t test for dependent samples to test the hypothesis that the mean number of monthly rentals has increased.

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## P-Value - Null Hypothesis - Productivity Data for plant worker productivity

See attached file.

11.51. A plant manager has collected productivity data for a sample of workers, intending to see whether there is a difference in the number of units they produce on Monday versus Thursday. The results (units produced) are in data file XR11051. Using the 0.01 level of significance, evaluate the null hypothesis that there is no difference in worker productivity between the two days. Identify and interpret the p-value for the test, then construct and interpret the 99% confidence interval for the mean difference in productivity between the days.
Worker Monday Thursday
1 49 46
2 56 59
3 63 65
4 52 57
5 47 45
6 67 71
7 71 70
8 45 49
9 42 43

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