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

What can you conclude at the $5\%$ significance level?

Short answer

At the $5\%$ significance level, there is adequate evidence to establish that the distribution of working hours of private practice doctors differs from the distribution of working hours of hospital doctors.

Step-by-step solution

Given information

The given data is

Explanation

From question $51$, $p-$value is $0.00051$

Assume the following hypothesis for the aforementioned test:

$H_0$: The working hours of private practice doctors are distributed in the same way that hospital doctors' working hours are distributed.

$H_1:$Private practice doctors' working hours are not distributed in the same way as hospital doctors' working hours are distributed.

Assume that the degree of significance is $\alpha =5\%$

$p-$value$\simeq 0<0.05$

The $p-$value is less than $\alpha ,H_0$is rejected.

At the $5\%$ significance level, there is adequate evidence to establish that the distribution of working hours of private practice doctors differs from the distribution of working hours of hospital doctors.