A recent sports game set a record for the number of television viewers. The game

Question

A recent sports game set a record for the number of television viewers. The game had a share of 76%,

meaning that among the television sets in use at the time of the game, 76%

were tuned to the game. The sample size is 25,798households. Use a 0.05 significance level to test the claim that more than 75%

of television sets in use were tuned to the sports game. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Explanation / Answer

here null hypothesis: p=0.75

alternate hypothesis: p>0.75

here n=25798

hence std error =(p(1-p)/n)1/2 =0.0027

hence test stat z=(phat-p)/std error =(0.76-0.75)/0.0027 =3.7093

for above test stat p value =0.0001

as p value is less then 0.05 level we reject null hypothesis,and conclude that

more than 75%

of television sets in use were tuned to the sports game

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