# A researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. A random sample of 32 workers at a large department store had a mean of 5.6. The standard deviation of the population is 1.2. Is there enough evidence to support the researcher's claim at a=0.01?

Question

A researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. A random sample of 32 workers at a large department store had a mean of 5.6. The standard deviation of the population is 1.2. Is there enough evidence to support the researcher's claim at a=0.01?

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Step 1

Hypotheses:

Let µ be the true average number of sick days a worker takes per year. The aim of the researcher is to check whether the number of sick days a worker takes per year is greater than 5 or not. The null and the alternative hypotheses are,

Step 2

The sample size is 32 that is greater than 30 and the population standard deviation is known as 1.2. Hence, z test can be used for testing the mean.

Test statistic:

The test statistic for hypothesis test for proportion is given by:

Step 3

Computing the test statistic for hypothesis te...

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