Of 200 youthful gamers (under 18) who tried the new Z-Box-Plus game, 160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over). The p-value for a right-tailed test to compare the two proportions would be approximately:

Question

Quizplus · Accepted Answer

We can use a two-sample z-test for proportions to compare the proportion of young gamers who rated the game as "excellent" (p1 = 160/200 = 0.8) to the proportion of adult gamers who did so (p2 = 144/200 = 0.72). The null hypothesis is H0: p1 = p2 and the alternative hypothesis is Ha: p1 > p2 (right-tailed test). Assuming independence and a large enough sample size for both groups, we can use the pooled sample proportion and standard error:

pooled proportion = (160 + 144)/(200 + 200) = 0.76
standard error = sqrt((0.76*(1-0.76)/200) + (0.76*(1-0.76)/200)) = 0.044
test statistic = (0.8 - 0.72)/0.044 = 1.82
p-value = P(Z > 1.82) ≈ 0.031

Therefore, the approximate p-value for the test is 0.031, which is closest to B).

Of 200 Youthful Gamers (Under 18) Who Tried the New