Question

Suppose you and three friends, Allan, Bella, and Chris, are designing a study to measure the approval rating of the current president. For each case, construct the desired confidence interval and briefly explain why the results are or are not valid.

(a) You poll 120 randomly selected people and find that 30 of them “approve”. You construct a 95% confidence interval for the proportion.

(b) Allan polls 200 people who he knows on Facebook and only 30 of them “approve”. He constructs a 90% confidence interval for the proportion.

(c) Bella polls 50 randomly selected people and finds that 7 of them “approve”. She constructs a 99% confidence interval for the proportion.

(d) Chris polls 400 randomly selected people and finds that 21 of them “approve”. He constructs a 99% confidence interval for the proportion.

(e) If the true approval rating of the president was 11%, which of the above confidence intervals does it lie in?

Answer 1