A poll conducted by YouGov between October 23-27, 2020 asked a
random sample of n = 1000 American adults “How concerned are you
that you or someone in your family will contract the coronavirus?”
67% of the respondents said that they were somewhat or very
concerned.
(a) Does this survey provide strong evidence that more than 60% of
American adults are somewhat or very concerned about contracting
the coronavirus? Write the null and alternative hypotheses, report
the test statistic and p-value, and state your conclusion using ? =
0.01.
(b) Calculate a 99% confidence interval for the population
proportion of American adults who are somewhat or very concerned
about contracting the coronavirus.
(c) Suppose YouGov wants to conduct a new poll next week, which
asks the same question. What sample size is needed so that margin
of error will be ±0.02 with 99% confidence?