Question

Game consoles: A poll surveyed

341

video gamers, and

72

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

26%

. Does the poll provide convincing evidence that the claim is true? Use the

=α0.05

level of significance and the

P

-value method with the TI-84 Plus calculator.

Part 1 of 4

Your Answer is correct

(a) State the appropriate null and alternate hypotheses.

:H0

=p0.26

  

:H1

≠p0.26

  

This hypothesis test is a  ▼two-tailed test.

Part: 1 / 4

1 of 4 Parts Complete

Part 2 of 4

(b) Compute the

P

-value. Round the answer to at least four decimal places.

P -value =

part 3 of 4

is it rejected or not?

Answer 1

Given that, n = 341 and x = 72

=> sample proportion = 72/341 = 0.2111

a) The null and alternative hypotheses are,

H0 : p = 0.26

H1 : p ≠ 0.26

This hypothesis test is a two-tailed test.

Test statistic is,

=> Test statistic = Z = -2.06

b) p-value = 2 * P(Z < -2.06) = 2 * 0.0197 = 0.0394

=> p-value = 0.0394

Since, p-value is less than significance level of 0.05, we reject the null hypothesis.