A poll surveyed 503 video gamers, and 106 of them said they prefer playing games on a console rather than a computer. An executive at a game console company claims that more than 25% of Gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the $\alpha = 0.05$ level of significance.
A) Yes
B) No
C) No conclusion is possible.

Question

Quizplus · Accepted Answer

We can conduct a one-sample proportion hypothesis test to determine whether the proportion of gamers who prefer consoles is greater than 0.25. Let p be the true proportion of gamers who prefer consoles. The null hypothesis is H0: p <= 0.25 and the alternative hypothesis is Ha: p > 0.25. We can use a z-test with the test statistic z = (p-hat - 0.25) / sqrt(0.25 * 0.75 / 503), where p-hat = 106/503 = 0.211. The p-value for this test is P(Z > (0.211-0.25) / sqrt(0.25 * 0.75 / 503)) = P(Z > -1.831) = 0.033, which is less than alpha = 0.05. Therefore, we reject the null hypothesis and conclude that there is evidence to suggest that more than 25% of gamers prefer consoles. However, the evidence is not strong since the p-value is only slightly less than 0.05.

A Poll Surveyed 503 Video Gamers, and 106 of Them α=0.05\alpha = 0.05α=0.05

A Poll Surveyed 503 Video Gamers, and 106 of Them $\alpha = 0.05$