Question

a study done by researchers at a university concluded that 70% of all student athletes in this country have been subjected to some form of hazing. The study is based on responses from 1200 athletes. What are the margin of error and 95% confidence interval for the study?

Answer 1

Answer:The margin of error is 0.01323 and 95% confidence interval is (0.674,0.73).

Explanation:

Since we have given that

p = 0.70

n = 1200

We need to find the margin of error;

Margin of error would be

`\sqrt{(p(1-p))/(n)}\\\\=\sqrt{(0.7* 0.3)/(1200)}\\\\=0.01323`

At 95% confidence level, α = 1.96

so, 95% confidence interval would be

`p\pm z* 0.01323\\\\=0.7\pm 1.96* 0.01323\\\\=0.7\pm 0.02593\\\\=(0.7-0.02593,0.7+0.02593)\\\\=(0.674,0.73)`

Hence, the margin of error is 0.01323 and 95% confidence interval is (0.674,0.73).