Question

In manufacturing, does worker productivity drop on Friday? In an effort to determine whether it does, a company’s personnel department randomly selects from a manufacturing plant five workers who make the same part. They measure their output on Wednesday and again on Friday and obtain the following results.

Worker	Wednesday Output	Friday Output
1	72	53
2	56	47
3	75	52
4	67	55
5	74	55

They use α = 0.05 and assume the difference in productivity is normally distributed. Do the samples provide enough evidence to show that productivity drops on Friday?

Round the intermediate values to 3 decimal places. Round your answer to 2 decimal places.

Observed t = ??

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=4.

Hence, it is found that the critical value for this left-tailed test is tc​=−2.132, for α=0.05 and df = 4df=4.

The rejection region for this left-tailed test is R={t:t<−2.132}.

t= -6.40

Decision about the null hypothesis: Since it is observed that t=−6.403<tc​=−2.132, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.0015, and since p=0.0015<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1​ is less than μ2​, at the 0.05 significance level.