Question

4. 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 pop- ulation 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. Shock ingly, 41% of the l 147 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? c. Your friend uses this data to build a confidence interval for the proportion of all U.S. men aged 18 to 55 who had not heard of the #meToo movement as of May 2018: (38.5%, 43.5%). What confidence level is associated with her interval?

Answer 1

a.

Sample proportion = 41% = 0.41

Sample size, n = 1147

Standard error of the sample proportion = $\sqrt{0.41 * (1 - 0.41)/1147} = 0.0145$

Z value for 95% CI is 1.96

Margin of error = 1.96 * 0.0145 = 0.02842 = 2.842%

b.

To get 1147 respondents, number of people (N) to be reached is given as,

N * 0.07 = 1147

N = 1147 / 0.07 = 16386 (Rounding to nearest integer)

c.

Margin of error = Width of confidence interval / 2 = (0.435 - 0.385) / 2 = 0.025

Estimated sample proportion = (0.435 + 0.385) / 2 = 0.41

For the sample size, n = 1147, the Standard error of the sample proportion is,

SE =  $\sqrt{0.41 * (1 - 0.41)/1147} = 0.0145$

Z value for the confidence level = Margin of error / Standard error = 0.025 / 0.0145 = 1.724

Using Z tables/calculator, the confidence level for z = 1.724 is  0.9153 = 91.53%