Question

A large nationwide company with 1200 employees claims that the number of days missed by its employees due to illness is below the national average of 7. A random sample of 40 employees resulted in a mean of 6.6 days with a standard deviation of 1.8. The hypothesis test resulted in a p-value of 0.084. Which of the following statements is true?

A. There is a 10% chance that the null hypothesis is true and a 8.3% chance that the alternative hypothesis is true.
B. There is a 8.3% chance that the mean number of days missed by employees at the company is below 7.
C. Since the probability that the mean number of days is below 7 is small, the null hypothesis is likely true.
D. If the mean number of days missed the company is 7 the probability of obtaining a sample mean of 66 days or lower is 0.063.

Answer 1

The last part of the question before the options is meant to be;

The hypothesis test using α = 0.1 resulted in a p-value of 0.084. Which of the following statements is true?

Answer:

B: There is a 8.3% chance that the mean number of days missed by employees at the company is below 7.

Explanation:

Significance value is α = 0.1

p-value = 0.084

Now, we want to test the claims that the number of days missed by its employees due to illness is below the national average of 7.

Now the p-value is basically a probability.

Thus, p = 0.084 can be written as 8.4%

It seems this 8.4 is an approximate version of 8.3 because the options use 8.3%.

Thus, Option B is the closest answer.