Question

A poll surveyed 341 video gamers, and 99 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 28%. Does the poll provide convincing evidence that the claim is true? Use the =α0.01 level of significance and the P-value method.

Answer 1

Game console manufacturing company claims that the proportion of gamers who prefer consoles differs from 28%.

H0 : proportion,p =0.28

Ha: p 0.28

Sample : 341 video gamers, and 99 of them said that they prefer playing games on a console i.e . = .2903

SD of proportion = == = 0.0243

t statistic = ( - p) / SD of proportion = (0.2903 -0.28 ) / 0.0243 = 0.4239

t /2 = =0.005 = 2.576 > t statistic , so p value is greater than =0.01

So, since p value is greater than significance level , we fail to reject null hypothesis.

The poll doesn't provide convincing evidence that the claim is true. Proportion doesn't differ from 28%.

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[ Not necessary but I am giving this for better understanding

t /2 = =0.025 = 1.96 > t statistic , so p value is greater than =0.05

t /2 = =0.25 = 0.674 > t statistic , so p value is greater than ​​​​​​​=0.5

If anyone want to find exact value then he can approximate this value from standard normal tablee since n is very large .

approx p value will be = 2 *(1- P(Z<.4239)) =2 * (1- .66276) =.67448 >0.01 ]