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 Table 4
20–30 30–40 40–50 50–60
Private
Practice
16 40 38 6
Hospital 8 44 59 39
Table 4
a. State the null and alternative hypotheses.
b. State the degree of freedom.
c. What is the test statistic?
d. What is the p-value?
e. What can you conclude at the 5% significance level?

Answer 1

a)  H₀: The distribution of working hours for private practice doctors is the same as the distribution of working hours for hospital doctors.

H_a: The distribution of working hours for private practice doctors is not the same as the distribution of working hours for hospital doctors.

b) rows -2, columns - 4

df=(rows-1)*(columns-1)=1*3=3

c) The expected data is given by

E_i=(row total*column total)/table total

20-30 30-40 40-50 50-60 Total

Private-practice 9.6 33.6 38.8 18.0 100

Hospital 14.4 50.4 58.2 27.0 150

Total 24 84 97 45 250

Using the tables of observed and expected data we can find the value of test statistic:

$\chi^2=\sum^8_{i=1}\frac{(Ob_i-Ex_i)^2}{Ex_i}=22.50368$

d)according to test statistic, the p value is 0.00005

e) since p-value is less that 0.05 (5% significance level), 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.