Question

A study done by highly professional statisticians shows that a popularity statistic of Avengers Endgame is 15% greater than the same statistic for the new season of Game of Thrones. To determine if this study was valid a DnD shop owner sent brochures to a simple random sample of 250 people on his Facebook friends list. He receives replies from 40 people which agree with the previous study. Does this evidence support the previous study? Use a 0.05 level of significance.

Answer 1

Here

H₀ : p = 0.15

H_a : p ≠ 0.15

Here sample statistic = p^ = 40/250 = 0.16

standard proportion = p₀ = 0.15

standard error of proportion = se_p = sqrt [p₀ * (1- p₀)/n] = sqrt [0.15 * 0.85/250] = 0.0226

Test statistic

Z = (p^ - p₀)/se_p

Z = (0.16 - 0.15)/0.0226 = 0.443

P - value = 2 * P(Z > 0.443) = 2 * 0.329 = 0.6580

Here P - value is greater than 0.05 level of significance so here we fail to reject the null hypothesis and conclude that the evidence support the previous study.