Question

A sample of 45 entrepreneurs worked an average of 52 hours a week. The population is approximately normally distributed with a standard deviation of 20 hours per week. You want to test whether there is sufficient evidence at the α = 0.10 significance level that entrepreneurs work more than 48 hours per week.

(a) Define the parameter to be tested.

(b) What is the null hypothesis (H0)? What is the alternative hypothesis (H1)?

(c) Specify the test statistic and identify its (approximate) distribution if H0 is true.

(d) Compute the observed value of the test statistic.

(e) Compute the p-value.

(f) Report the strength of the evidence against H0 in favour of H1.

(g) Report the estimated value of the parameter along with the estimated standard error.

(h) If we are asked to test H0 at the significance level α, compare α with the p-value and reject H0 exactly when the p-value ≤ α. Explain your decision in terms of the number of hours worked per week by entrepreneurs.

Answer 1

a) Let denotes the average working hours a week for entrepreneurs.

Parameter to be tested :

b) - h)

There is sufficient evidence to support the claim that entrepreneurs work more than 48 hours per week.