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 57 day shift workers was 359. The mean number of unts produced by a sample of 65 night shifters was 369. Assume the population standard deciation of the number of units produced on the day shift is 23 and 32 on the night shift.

At the .05 sig level id the number of units produced on the night shift larger

a. is this a one tailed or 2 tailed test?

b. state the decision rule. round 2 decimal places

the decision rule is to reject if z<

c. compute the value of the test statistic round to 2 decimals

d. what is your decision regarding h0? reject/do not reject

Answer #1

The statistical software output for this problem is:

**Two sample Z summary hypothesis test:**

?_{1} : Mean of population 1 (Std. dev. = 23)

?_{2} : Mean of population 2 (Std. dev. = 32)

?_{1} - ?_{2} : Difference between two means

H_{0} : ?_{1} - ?_{2} = 0

H_{A} : ?_{1} - ?_{2} < 0

**Hypothesis test results:**

Difference |
n_{1} |
n_{2} |
Sample mean |
Std. err. |
Z-stat |
P-value |
---|---|---|---|---|---|---|

?_{1} - ?_{2} |
57 | 65 | -10 | 5.0034536 | -1.9986195 | 0.0228 |

Hence,

a) One tailed

b) Decision rule: z < -1.96

c) Test statistic = -2.00

d) Reject

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H0 : μd ≤ 0
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1
2
3
4
Day shift
11
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4
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