Question

Do private practice doctors and hospital doctors have the same distribution of working hours? Suppose that a sample of 100 private practice doctors and 150 hospital doctors are selected at random and asked about the number of hours a week they work. The results are shown in the table below.

	20–30	30–40	40–50	50–60
Private Practice	16	40	38	6
Hospital	8	44	59	39

A. State the null and alternative hypotheses.

B. What is the test statistic? (Round your answer to two decimal places.)

C. What can you conclude at the 5% significance level? (from the following- We reject the null hypothesis. There is enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors. ---We fail to reject the null hypothesis. There is enough evidence to show that the number of hours worked is dependent on the type of doctor. ---- We fail to reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.----We fail to reject the null hypothesis. There is not enough evidence to show that the number of hours worked is dependent on the type of doctor. ---- We reject the null hypothesis. There is not enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.)

Answer 1

A)

Null hypothesis:Ho:private practice doctors and hospital doctors have the same distribution of working hours

Alternate hypothesis: Ha: private practice doctors and hospital doctors do not have the same distribution of working hours

B)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	20-30	30-40	40-50	50-60	Total
	private practice	9.60	33.60	38.80	18.00	100.00
	hospital	14.40	50.40	58.20	27.00	150.00
	total	24.00	84.00	97.00	45.00	250.00
chi square    χ2	=(Oi-Ei)2/Ei	20-30	30-40	40-50	50-60	Total
	private practice	4.27	1.22	0.02	8.00	13.5022
	hospital	2.84	0.81	0.01	5.33	9.0015
	total	7.1111	2.0317	0.0275	13.3333	22.504
test statistic X2 =		22.504

C)

We reject the null hypothesis. There is enough evidence to show that the distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors