8.3.31-T Question Help Arecent sports game set a record for the number of televi

Question

8.3.31-T Question Help Arecent sports game set a record for the number of television viewers. The game had a share of 78%, meaning that among the television sets in use at the time of the game, 78% were tuned to the game. The sample sze is 25.062 households Use a 0.01 significance level to test te claim that more than 74% of television sets in use were tuned to the sports game. Identify the null hypothesis, altemative 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. Which of the following is the hypothesis test to be conducted? OA. H0: p=0.74 OB. Ho: p> 0.74 H1 : p#0.74 Ho:p=0.74 H:p0.74 ° C. Ho:p#0.74 D. H1 : p=0.74 E. Ho: p

Explanation / Answer

Here we will see first that which type of test it is.

(i) Two tailed test

(ii) Left or right tailed test

Here Hypthesis are

H0 : p = 0.74

Ha = p > 0.74

option a is correct.

Here sample proportin p^ = 0.78

sample size = 25062

standard error of the proportion is se0 = sqrt [ 0.74 * 0.26/ 25062] = 0.00277

Test statistic

Z = (0.78 - 0.74)/ 0.00277 = 14.44

so p - value = Pr( Z > 14.44) = 0.0000

so the p - value is less than 0.01 significance level.

so we shall reject the null hypothesis and can conclude that the share of television share is more than 74%

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