A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task is faster if they are wearing earbuds. A random sample of 20 workers' times were collected before and after wearing earbuds. Test the claim that the time to complete the task will be faster, i.e. meaning has production increased, at a significance level of α = 0.01 For the context of this problem, μD = μbefore−μafter where the first data set represents before earbuds and the second data set represents the after earbuds. Assume the population is normally distributed. The hypotheses are: H0: μD = 0 H1: μD > 0 You obtain the following sample data:
Before |
After |
---|---|
68 |
62.3 |
72.5 |
61.6 |
39.3 |
21.4 |
67.7 |
60.4 |
38.3 |
47.9 |
85.9 |
78.6 |
67.3 |
75.1 |
59.8 |
48.3 |
72.1 |
65 |
79 |
83 |
61.7 |
56.8 |
57.9 |
44.7 |
56.8 |
50.6 |
71 |
63.4 |
80.6 |
68.9 |
59.8 |
33.9 |
73.1 |
79 |
49.9 |
38.4 |
59.2 |
55.4 |
64.8 |
55.6 |
Choose the correct decision, summary and state the p-value.
Do not reject H_{0}, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0012
Reject H_{0}, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0024
Reject H_{0}, there is enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0012
Do not reject H_{0}, there is not enough evidence to support the claim that the time to complete the task has decreased when workers are allowed to wear earbuds at work and the p-value = .0024.
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