Question

Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. The mean number of units produced by a sample of 50 day-shift workers was 353. The mean number of units produced by a sample of 55 night-shift workers was 363. Assume the population standard deviation of the number of units produced on the day shift is 25 and 31 on the night shift.

At the 0.01 significance level, is the number of units produced on the night shift larger?

1. Is this a one-tailed or a two-tailed test?

• One-tailed test
• Two-tailed test

2. State the decision rule. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀.
• Do not reject H₀.

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Answer 1

Solution:

Given:

Night Shift:

Sample Size = n1 = 55

Sample mean =

Population Standard Deviation =

Day Shift:

Sample Size = n2 = 50

Sample mean =

Population Standard Deviation =

significance level = 0.01

We have to test whether there are more units produced on the night shift than on the day shift.

Part a) Is this a one-tailed or a two-tailed test?

Since we have to test if there are more units produced on the night shift than on the day shift, this is directional statement, hence this is One tailed test and it is Right tailed test.

Part b) State the decision rule:

Find z critical value for significance level = 0.01

Since this is right tailed test : Find Area = 1 - 0.01 = 0.99

look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_c = 2.33

Thus decision rule is:

Reject H0, if z test statistic value > z critical value = 2.33, otherwise we fail to reject H0.

Part c) Compute the value of the test statistic.

Part d) What is your decision regarding H₀?

Since z test statistic value = z = 1.83 < 2.33 , we failed to reject H₀.

That is : Do not reject H₀.