In a random sample of 300 Canadian women,68% watch CBC News.In a random sample of 200 Canadian men,56% watch CBC News.Construct a 98% confidence interval for the difference in the proportions of women and men who watch CBC News.

Question

Quizplus · Accepted Answer

We can use the two sample z-test for the difference in proportions:
z = (0.68 - 0.56) / sqrt[(0.68 * 0.32 / 300) + (0.56 * 0.44 / 200)] = 3.06
Using a standard normal distribution table or calculator, the p-value is approximately 0.002, which is less than 0.02 (1 - 0.98). Therefore, we reject the null hypothesis and conclude that there is a significant difference in the proportions of women and men who watch CBC News.
The 98% confidence interval can be calculated as:
(0.68 - 0.56) ± 2.33 * sqrt[(0.68 * 0.32 / 300) + (0.56 * 0.44 / 200)]
= 0.12 ± 0.053
= (0.067, 0.173)
The best choice is (C) (0.017, 0.223), which is the closest range to (0.067, 0.173) among the options given.

In a Random Sample of 300 Canadian Women,68% Watch CBC