Question

Game consoles: A poll surveyed 341 video gamers, and 95 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An executive at a game console manufacturing company claims that the proportion of gamers who prefer consoles differs from . Does the poll provide convincing evidence that the claim is true

Answer 1

proportion of gamers who prefer console does not differ from 29%

Explanation:

Given :

n = 341 ; x = 95 ; Phat = x / n = 95/341 = 0.279

H0 : p = 0.29

H1 : p ≠ 0.29

The test statistic :

T = (phat - p) ÷ √[(p(1 - p)) / n]

T = (0.279 - 0.29) ÷ √[(0.29(1 - 0.29)) / 341]

T = (-0.011) ÷ √[(0.29 * 0.71) / 341]

T = -0.011 ÷ 0.0245725

T = - 0.4476532

Using the Pvalue calculator from test statistic score :

df = 341 - 1 = 340

Pvalue(-0.447, 340) ; two tailed = 0.654

At α = 0.01

Pvalue > α ; We fail to reject the null and conclude that there is no significant evidence that proportion of gamers who prefer console differs from 29%