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 79%, meaning that among the television sets in use at the time of the game, 79% were tuned to the game. The sample size is 25, 041 households. Use a 0.05 significance level to test the claim that more than 73% of television sets in use were turned to the sports game. Identify the null hypothesis, alternative hypothesis, P-value, conclusion about the null hypothesis, and final conclusion that the addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution. Which of the following is the hypothesis test to be conducted? A. H_0: p = 0.73 H_1: p notequalto 0.73 B. H_0: p = 0.73 H_1: p 0.73 H_1: p = 0.73 D. H_0: p 0.73 What is the P-value? P-value ____ (Round to four decimal places as needed.) What is the conclusion on the null hypothesis? Reject the null hypothesis because the P-value is greater than the significance level alpha. Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, alpha. a Reject the null hypothesis because the P-value is less than or equal to the significance level, alpha. Fail to reject the null hypothesis because the P-value is greater than the significance level alpha.

Explanation / Answer

(a) Option F

(b)

Data:    

n = 25041   

p = 0.73   

p' = 0.79   

Hypotheses:   

Ho: p 0.73   

Ha: p > 0.73   

Decision Rule:   

= 0.05   

Critical z- score = 1.644853627

Reject Ho if z > 1.644853627

Test Statistic:   

SE = {(p (1 - p)/n} = (0.73 * (1 - 0.73)/25041) = 0.002805547

z = (p' - p)/SE = (0.79 - 0.73)/0.0028055465439175 = 21.38620731

p- value = 0.0000

(c) Decision:

Since 21.386207 > 1.644853627 we reject Ho

Conclusion:

Option C.

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