Question

1. The English Labor Minister thinks the average factory worker misses more than 7 days of work each year. He hires a research firm to conduct a study of unexcused absenteeism among factory workers. Their sample of 115 workers in English factories had a mean number of days absent of 9.88 and the standard deviation was 17.75 days.

a) Is there sufficient evidence at alpha=.05 to support the Minister’s hypothesis? (10 points)
b) Is there sufficient evidence at alpha=.01 to support the Minister’s hypothesis (yes or no)? Explain.**You do not need to repeat all 5 steps for this part, just explain how you came to your conclusion (1 point)

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 7
Alternative Hypothesis, Ha: μ > 7

Rejection Region
This is right tailed test, for α = 0.05 and df = 114
Critical value of t is 1.658.
Hence reject H0 if t > 1.658

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (9.88 - 7)/(17.75/sqrt(115))
t = 1.74

P-value Approach
P-value = 0.0423
As P-value < 0.05, reject the null hypothesis.

b)

P-value Approach
P-value = 0.0423
As P-value >0.01, fail to reject the null hypothesis.