Question

Gender pay gap in medicine. A study examined the average pay for men and women entering the workfor4ce as doctors for 21 different positions. If each gender was equally paid, then we would expect about half of those positions to have men paid more than women and women would be paid more than men in the other half of positions. Write appropriate hypotheses to test this scenario. H 0 : p = Incorrect H A : p ≠ Incorrect Men were, on average, paid more in 19 of those 21 positions. complete a hypothesis test using the hypotheses above. Check the sample size to verify that we can use the normal model to answer this question. n p 0 = Incorrect (Round to one decimal place, if necessary.) n ( 1 − p 0 ) = Incorrect (Round to one decimal place, if necessary.) Calculate the standard error of the estimate. σ ˆ p = Incorrect (Round to four decimal places, if necessary.) Calculate the p-value. p-value: Incorrect (Round to four decimal places, if necessary.)

Answer 1

(a)

Appropriate hypotheses to test this scenario:

H0: Null Hypothesis: p = 0.5

HA: Alternative Hypothesis: p 0.5

(b)

n = Sample Size = 21

To check the sample size to verify that we can use the normal model to answer this question:

np₀ = 21 X 0.5 = 10.5 > 10

n (1 - p₀) = 21 X (1 - 0.5) = 10.5 > 10

Thus, both conditions are satisfied.

(c)

The standard error of the estimate is given by:

(d)

= Sample Proportion = 19/21 = 0.9048

Test Statistic is given by:

Z = (0.9048 - 0.5)/0.1091

= 3.7104

Table of Area Under Standard Normal Curve gives area = 0.4999

So,

p - value = (0.5 - 0.4999) X 2 = 0.0002

So,

p - value = 0.0002