Answer to Question #261068 in Statistics and Probability for Elop

Question

A poll of 400 Califorinans found that 83% were in favor of a mandatory 14-day quarantine for anyone who has come into contact with a person who tested positive for COVID-19. Use the z-test with a level of significance =.025 to test the claim that more than 80% of Califorinans are in favor of the mandatory 14-day quarantine period. >Z-table

Answer 1

$n=400 \\ \hat{p} = 0.83 \\ α=0.025 \\ H_0: p ≤ 0.80 \\ H_1: p > 0.80$

Test-statistic

$Z = \frac{\hat{p} -p}{\sqrt{\frac{p(1-p)}{n}}} \\ = \frac{0.83-0.80}{\sqrt{\frac{0.80(1-0.80)}{400}}} \\ = 1.5$

P-value = P(Z> 1.5) = 0.0668

P-value > α (0.025)

Fail to reject the null hypothesis.

There is enough evidence to claim that more than 80 % of Califorinans are in favor of the mandatory 14-day quarantine period.