Question

A poll surveyed 341 video gamers, and 85 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 less than 26% of gamers prefer consoles. Does the poll provide convincing evidence that the claim is true? Use the =α0.10 level of significance and the P-value method with the Cumulative Normal Distribution Table.

(a) State the appropriate null and alternate hypotheses.

H0:

H1:

This hypothesis test is a _

(b) Compute the value of the test statistic. Round the answer to at least three decimal places.

(c)Determine whether to reject H0.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.26

H_a : p < 0.26

= x / n = 85 / 341 = 0.2493

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2493 - 0.26 / [(0.26 * 0.74) / 341]

= -0.452

This hypothesis test is a one tailed test .

P-value = 0.3257

= 0.10

P-value >

Fail to reject H0