Question

I am looking at a study on rape culture and writing an essay on it. One of the questions asks to prove the argument come up with an instance where you think a confidence interval, hypothesis test, or regression would help? Here are the numbers I have from the study:

sample size: 483

37% of the 483 said they had been a victim to rape over the course of their first year.

I am confused on which method I should use and how I would get the numbers for it

Answer 1

Solution:

For the given scenario, you should use confidence interval for the population proportion. You are not given the claimed value for the population proportion, so you do not use hypothesis test. Also, you cannot use regression, because we need two variables for regression.

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given n = 483, P = 0.37

We assume 95% confidence interval.

Z = 1.96 (by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = 0.37 ± 1.96* sqrt(0.37*(1 – 0.37)/483)

Confidence Interval = 0.37 ± 1.96* 0.0220

Confidence Interval = 0.37 ± 0.0431

Lower limit = 0.37 - 0.0431 = 0.3269

Upper limit = 0.37 + 0.0431 = 0.4131

Confidence interval = (0.3269, 0.4131)

We are 95% confidence that the proportion of the students said that they had been a victim to rape over the course of their first year will be lies within 32.69% and 41.31%.