Chapter 8, Problem 84CRE

Television In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, $38\%$ responded yes. In 2018, $31\%$ said it would be very hard to give up watching television.

a. Assume that both polls used samples of 200 people. Do a test to see whether the proportion of people who reported it would be very hard to give up watching television was significantly different in 2002 and 2018 using a $0.05$ significance level.

b. Repeat the problem, now assuming the sample sizes were both 2000. (The actual sample size in 2018 was 2002.)

c. Comment on the effect of different sample sizes on the p-value and on the conclusion.