A recent sports game set a record for the number of television viewers. The game
ID: 3153338 • Letter: A
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 24,398 households. Use a 0.050 significance level to test the claim that more than 74% 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.What is the test statistic?What is the P-value?What is the conclusion on the null hypothesis?What is the final conclusion?
Explanation / Answer
A)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.74
Ha: p > 0.74
******************************
As we see, the hypothesized po = 0.74
Getting the point estimate of p, p^,
p^ = x / n = 0.76
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.002808183
Getting the z statistic,
z = (p^ - po)/sp = 7.122042735 [ANSWER, TEST STATISTIC]
****************************
As this is a 1 tailed test, then, getting the p value,
p = 5.31695*10^-13 [ANSWER, P VALUE]
***************************
As P is very small, we REJECT THE NULL HYPOTHESIS. [ANSWER, DECISION ABOUT THE NULL HYPOTHESIS]
************************
Hence, there is significant evidence that more than 74% of television sets in use were tuned to the sports game. [CONCLUSION]