Question

A researcher wishes to see if the average number of sick days a worker takes per year is greater than 2.8. A random sample of 30 workers at a large department store had a mean of 3.1. The standard deviation of the population is 0.8. Is there enough evidence to support the researchers claim at α = 0.01?

Answer 1

This hypothesis test is a right tailed test .

The null and alternative hypothesis is

H₀ : $\mu$ = 2.8

H_a : $\mu$ > 2.8

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$    / $\sqrt$ n

= (3.1 - 2.8) / 0.8 / $\sqrt$ 30

Test statistic = 2.054

P-value = 0.02

P-value > $\alpha$

Fail to reject the null hypothesis .

There is not enough evidence to support the researchers claim at α = 0.01 .