Tnals n an expenment with?polygraph include g7 results that ncude 23 ceses of wr

Question

Tnals n an expenment with?polygraph include g7 results that ncude 23 ceses of wrong results ?na 74 cases ot correct resuits us 0.01 sonmcence level to test the claim that such polygraph results ne correct iess than 8 % ot the time Identity the null hypothesis, altermative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusicn that addresses the original clairm. Use the P-value iethod. Use the norrnal distribution as an approximation of the binomial distribution Let p b the population proporton of correct poygraph results. Identify the null and alternative hypotheses. Choose th correct enswer below A. Ho:p 0.80 H, pDaO C. Ho: p-0.30 B. H: p 0.80 OD. Ho-p-0.20 OF. Hop 020 E. Hn.p:0.20 H1 P 020 The test statistic is zRound to two decimal places as needed.) The P-value is | |.?ound to four decimal places as needed. Identity the concus?on about th null hypothesis end the tinal conclusion that Eddresses the onginal Claim ? | H0. There | ? sufficient evidence to support the claim tnat te polygraph results are correct less than 80% of the tine

Explanation / Answer

Option-B) H0: p = 0.8

H1: p < 0.8

p^ = 74/97 = 0.763

n = 97

SE = sqrt(p * (1 - p) / n) = sqrt(0.8 * 0.2 / 97) = 0.0406

The test statisic, Z = (p^ - p) / SE = (0.763 - 0.8) / 0.0406 = -0.91

P-value = P(Z < -0.91) = 0.1814

Since p-value is not less than , 0.01 we should not reject null hypothesis

Do not reject H0. There is not sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time

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