Question

Interested in social justice? If so, one difficulty you’ll face is exposure. Even in today’s social-media-obsessed and news-heavy climate, it is difficult to get a large percentage of the population to know about a given issue. As an example, in May 2018 Glamour and GQ magazines co-conducted a poll to see what percentage of men had heard of the #meToo movement. Shockingly, 41% of the 1147 men (aged 18 to 55) reported that they had never heard of this!

a. What margin of error should the pollsters report assuming they are using approximate 95% CIs?

b. Another challenge you face with social justice issues is people’s unwillingness to participate in surveys. If a random American man (aged 18 to 55) has a 7% chance of agreeing to your interview, how many people do you expect to reach out to if your goal is to have 1147 respondents? (A non-integer answer is possible.)

Answer 1

Here Sample size n = 1147

Probability that men never heard about the issue = p = 0.41

so here the distribution is binomial and we are approximating it to normal.

(a) Here,

margin of error = critical test statistic * standard error of sample mean

critical test statistic for 95% confidence interval = 1.96

standard error of sample mean = sqrt [p * (1-p)/n] = sqrt [0.41 * (1-0.41)/1147] = 0.0145

Margin of error = 0.0145 * 1.96 = 0.0285

so report should report a margin of error of 2.85%

(b) Pr(Chance of agreeing to our interview) = 0.07

Total respondents to be achived = 1147

So, expected number of people to reach out to have 1147 respondents = 1147/0.07 = 16385.71