Question

A reseacher wishes to see if the average number of sick days a worker takes per year is greater than 5. A random sample of 26 workers at a large department store had a mean of 5.2. The standard deviation of the population is 1.3. Is there enough evidence to support the researcher's claim at a = 0.05? Assume that the variable is normally distributed. Use the critical value method with tables. State the hypotheses and identify the claim with the correct hypothesis.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 5

H_a : > 5

Test statistic = z

= ( - ) / / n

= (5.2 - 5) / 1.3 / 26

Test statistic = 0.78

P(z > 0.78) = 1 - P(z < 0.78) = 0.2177

P-value = 0.2177

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not enough evidence to support the researcher's claim at a = 0.05 .