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. You may use technology to compute your answers. 20–30 30–40 40–50 50–60 Total Private Practice 16 40 38 94 Hospital 8 44 59 111 Total 24 84 97 205

Question

22-06-2021
Mathematics

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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. You may use technology to compute your answers. 20–30 30–40 40–50 50–60 Total Private Practice 16 40 38 94 Hospital 8 44 59 111 Total 24 84 97 205

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amcool amcool · Answer 1 · 2021-06-24T21:54:19+02:00

Answer:

1. The correct option is:

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

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

2. The test statistic is -0.97.

3. The correct option is E. 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.

Step-by-step explanation:

Note: This question is not complete and it contains some inconsistency errors in thee data. The correct complete question is therefore provided before answering the question. See the attached pdf for the correct complete question.

The explanation of the answer is now provided as follows:

1. State the null and alternative hypotheses.

Since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is:

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

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

2. What is the test statistic?

Note: See the attached excel file for the calculation of total of (f1 * x), total of (f2 * x), total of (f1 * x^2) and total of (f2 * x^2).

From the attached excel file, we have:

N2 = Total of f2 = Sample size of Hospital = 150

M1 = Mean of Private-Practice = Total of (f1 * x) / N1 = 38.40

M2 = Mean of Hospital = Total of (f2 * x) / N2 = 43.60

S1^2 = Variance of Private-Practice = Total of (f1 * x^2) / N1 = 1,541.00

S2^2 = Variance of Hospital = Total of (f2 * x^2) / N2 = 1,975.67

Therefore, we have:

t = (M1 - M2) / ((S1^2 / N1) + (S2^2 / N2))^0.5 = (38.40 - 43.60) / ((1,541 / 100) + (1,975.67 / 150))^0.5 = -0.97

Therefore, the test statistic is -0.97.

3. What can you conclude at the 5% significance level?

At 5% significance level, the test statistic from the Z distribution table known as t-tab is 1.96.

Since our calculated test statistic is -0.9727 is less than 1.96, this implies that we fail to reject the null hypothesis (H0).

Again, since we are trying to examine whether private practice doctors and hospital doctors have the same distribution of working hours, this implies that the correct option is E. 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.