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 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.) 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)

n = 1147    

p = 0.41    

% = 95    

Standard Error, SE = √{p(1 - p)/n} =    √(0.41(1 - 0.41))/1147 = 0.014522327

z- score = 1.959963985    

margin of error = z * SE =     1.95996398454005 * 0.0145223274570216 = 0.02846324 ( 2.85%)

(b)

Number of people = (100/7) * 1147 = 16385.71 (16386 people)

(c)

43.5% means 0.435

0.435 = 0.41 + z * √(pq/n)

0.435 - 0.41 = z * √(0.41 * 0.59/1147)

0.025 = z * 0.0145

z = 1.7241, which corresponds to a confidence interval of 91.53%