It has always been difficult to attract general physicians to rural areas. Small

Question

It has always been difficult to attract general physicians to rural areas. Small-town doctors do not have the opportunity to take much time off, and the salary is relatively low. However, the quality of life is often appealing. Past records indicate that 52% of all physicians in rural areas leave after one year. The federal government has decided to offer more incentives for doctors to stay in rural areas, for example, loan forgiveness and housing allowances. A few years after this program was implemented, a random sample of rural-area physician positions showed 62 of 130 left after one year. a. Identify n, x, and p_0 b. Check the nonskewness criterion. Is a large-sample hypothesis test about p appropriate? c. Conduct the appropriate test to determine whether the turnover rate of rural doctors has decreased. Use alpha = 0.01. d. Compute the p value associated with this test.

Explanation / Answer

a) sample size, n = 130, number of success, x = 62 and hypothesised mean, p0 = 0.52

b) To approximate using normal, we require n*p0 >=10 and n*(1 - p0 >= 10
130*0.52 = 67.6 and 130*0.48 = 62.4. Therefore large sample hypothesis test for p is appropriate

c) p = 62/130 = 31/65

H0: p0 = 0.52
Ha: p0 < 0.52

standard deviation, = sqrt[ p0 * ( 1 - p0 ) / n ] = sqrt(0.52*0.48/130) = 0.0438178

z = (p - p0) / = (31/65 - 0.52)/0.0438178 = -0.98309

d) p = 0.1628
p > 0.01, Fail to reject null hypothesis. There is insufficient evidence to support the hypothesis that turnover rate has decreased.

Reject the null hypothesis. We have

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