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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:
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:
Then, we can calculate the z-statistic as:
This test is a left-tailed test, so the P-value for this test is calculated as:
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.