Q. 50 Do private practice doctors and ... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 11: Q. 50 (page 657)

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 is the test statistic?

Short Answer

Expert verified

The value of test statistic is $22.50368 .$

Step by step solution

Given information

The given data is

Explanation

From the given table

$\begin{array}{l} Given Table (Observed Frequency) \\ 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & Total \\ Private Practice & 16 & 40 & 38 & 6 & 100 & Row Total \\ Hospital & 8 & 44 & 59 & 39 & 150 \\ Total & 24 & 84 & 97 & 45 & 250 \\ Column total \end{array}$

The formula to calculate the expected frequency is

$E = \frac{(r o w t o t a l) (c o l u m n t o t a l)}{G r a n d t o t a l}$

$\begin{array}{l} Expected Frequency \\ 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & Total \\ Private Practice & \frac{24 (100)}{250} = 9.6 & \frac{84 (100)}{250} = 33.6 & \frac{97 (100)}{250} = 38.8 & \frac{45 (100)}{250} = 18 & 100 \\ Hospital & \frac{24 (150)}{250} = 14.4 & \frac{84 (150)}{250} = 50.4 & \frac{97 (150)}{250} = 58.2 & \frac{45 (150)}{250} = 27 & 150 \\ Total & 24 & 84 & 97 & 45 & 250 \end{array}$

Test statistics $= 鈭� \frac{(O - E)^{2}}{E}$

Therefore, test statistic is

$= (13.50221 + 9.001473) o r (7.11111 + 2.03175 + 0.02749 + 13.33333) = 22.50368 .$

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