An average computer mouse inspector can inspect 40 mice per hour. The 46 computer mice inspectors at a particular factory can only inspect 36 mice per hour with a standard deviation of 8. Does the company
Have reason to believe that these inspectors are slower than average?
A) Yes, because -3.39 falls in the noncritical region
B) No, because -1.95 falls in the critical region
C) Yes, because -3.39 falls in the critical region
D) No, because -1.95 falls in the noncritical region

Question

Quizplus · Accepted Answer

We need to conduct a one-sample z-test to determine if the sample of 46 inspectors is significantly different from the population mean of 40 inspectors per hour.

Our hypotheses are:
Null Hypothesis (H0): The mean inspection rate of the 46 inspectors is not significantly different from the population mean of 40 mice per hour.
Alternative Hypothesis (Ha): The mean inspection rate of the 46 inspectors is significantly lower than the population mean of 40 mice per hour.

We can calculate the test statistic as:
z = (x̄ - μ) / (σ / √n)
where x̄ is the sample mean (36), μ is the population mean (40), σ is the population standard deviation (8), and n is the sample size (46).

z = (36 - 40) / (8 / √46)
z = -3.39

Using a significance level of 0.05, and a two-tailed test, the critical value for rejection is ±1.96. Since -3.39 falls within the critical region, we reject the null hypothesis and conclude that there is evidence to suggest that the mean inspection rate of the 46 inspectors is significantly lower than the population mean of 40 mice per hour. Therefore, the answer is C.

An Average Computer Mouse Inspector Can Inspect 40 Mice Per