Question

A poll surveyed 341 video gamers, and 95 of them said 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 gamer who prefer consoles differs from 29%. Does the poll provide convincing evidence that the claim is true? Use the a= 0.05 level of significance and the P- method with the TI -84 Calculator.

Answer 1

I do not own a TI84 calculator so have solved the problem by hand:

The following information is provided: The sample size is N=341, the number of favorable cases is X=95, and the sample proportion is , and the significance level is α=0.05

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

This corresponds to a two-tailed test, for which a z-test for one population proportion needs to be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a two-tailed test is zc​=1.96.

The rejection region for this two-tailed test is R={z:∣z∣>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that ∣z∣=0.464≤zc​=1.96, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.6425, and since p=0.6425≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than p0​, at the α=0.05 significance level.

Graphically

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