Question

A researcher wishes to see if the average number of sick days a worker takes per year is less than 5. A random sample of 30 workers at a large department store had a mean of 4.8. The standard deviation of the population is 1.2 days. Is there enough evidence to support the claim at alpha = 0.01?

Answer 1

Answer:

No. At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the average number of sick days a worker takes per year is significantly less than 5.

Then, the null and alternative hypothesis are:

$H_0: \mu=5\\\\H_a:\mu< 5$

The significance level is 0.01.

The sample has a size n=30.

The sample mean is M=4.8.

The standard deviation of the population is known and has a value of σ=1.2.

We can calculate the standard error as:

$\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.2}{\sqrt{30}}=0.219$

Then, we can calculate the z-statistic as:

$z=\dfrac{M-\mu}{\sigma_M}=\dfrac{4.8-5}{0.219}=\dfrac{-0.2}{0.219}=-0.913$

This test is a left-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z$

As the P-value (0.181) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.01, there is not enough evidence to support the claim that the average number of sick days a worker takes per year is significantly less than 5.