SOLUTION: This question has been submitted several times, will someone please help. The company claims that its new drug is equally effective for preventing colds for men and women. To tes

Click here to see ALL problems on Probability-and-statistics

Question 960762: This question has been submitted several times, will someone please help.
The company claims that its new drug is equally effective for preventing colds for men and women. To test this claim, the researchers chose a simple random sample of 100 women and 200 men. At the end of the study, 38% of the women caught a cold, and 51% of the men caught a cold. Test the company's claim. Use alpha = 0.05.
A) state the null and alternative hypothesis, B) determine the critical value(s) that define the rejection region, C) calculate the value of the test statistic, D) make the decision to reject the null hypothesis or not, and E) state a full conclusion, in context.
Please, please help.

Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website!

A) H₀: p₁ = p₂ H_a: p₁ ≠ p₂ ----------------------------------------- B) The rejection region will be |z| > 1.96 or if you prefer z < -1.96 or z > 1.96 ----------------------------------------- (C)

At the end of the study, 38% of the women caught a cold, and 51% of the men caught a cold.

Since we are testing effectiveness in preventing a cold, not in catching a cold, we subtract from 100% and consider this as saying that 62% of the women did not catch a cold, and that 49% of the men did not catch a cold. Since there were 100 women, then or 62 women did not catch cold. Since there were 200 men, then or 98 men did not catch cold. Substitute those values in the formula below to find z. ------------------------------- (D) 2.1276 is greater than 1.96, so we reject the null hypothesis. ------------------------------- (E) There is a significant difference between the effectiveness of the new drug for cold prevention in women and its effectiveness for cold prevention in men. Edwin