Two AP Statistics Questions

Question

Question 1:

A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

Question 2:

A large company is being sued for gender discrimination because 20% of newly hired candidates are women when 40% of all applicants were women. You plan to use hypothesis testing to determine whether there is significant evidence that the company's hiring practices are discriminatory.

Part A: State the null and alternative hypotheses for the significance test.

Part B: In the context of the problem, what would a Type I error be? A Type II error?

Part C: If the hypothesis is tested at a 1% level of significance instead of 5%, how will this affect the power of the test?

Part D: If the hypothesis is tested based on the hiring of 1,000 employees rather than 100 employees, how will this affect the power of the test?

Answer 1

Question 1:

Ho: p = 0.75

Ha: p < 0.75

sample size (n) = 150

sample proportion phat = 100/150 = 0.67

conditions for normal assumption: > 10 successes and failures (we have 100 and 50 of each, so assumption met)

z = (phat - p)/sqrt(p*(1-p)/n) = (0.67 - 0.75)/sqrt(0.75*0.25/150) = -2.26

left-side test, so critical value at 0.05 is -1.645, so Ho is rejected.

Question 2:

Ho: p = 0.40

Ha: p < 0.40

type I error: reject null hypothesis when it is true - conclude discriminatory when not

type II error - do not reject null hypothesis when it is false - do not conclude discriminatory when it is

lower level of significance increases probability of type II error, which in turn lowers the power (the probability of a true positive result)

increase in sample size increases the power of the test