37. Trials in an experiment with a polygraph include 99 results that include 23

Question

37. Trials in an experiment with a polygraph include 99 results that include 23 cases of wrong results and 76 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80% of the time.(a) Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. ,? (b) test statistic,? P-value?,(c) conclusion about the null hypothesis? (d) Identify the level of significance .? (e)and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.(f) Determine if the test is left-tailed, right-tailed, or two-tailed

36.In a study of 420,138 cell phone users, 106 subjects developed cancer of the brain or nervous system. Test the claim of a somewhat common belief that such cancers are affected by cell phone use. That is, test the claim that cell phone users develop cancer of the brain or nervous system at a rate that is different from the rate of 0.0340% for people who do not use cell phones. Because this issue has such great importance, use a 0.005 significance level. 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.

35.A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this writing, 294 babies were born to parents using the new method, and 228 of them were boys. Use a 0.050 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. 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.

34A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this writing, 964 babies were born to parents using the new method, and 868 of them were girls. Use a 0.050 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. 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

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Let P be the proportion of correct results of all polygraph results

a) H0: P 0.80
Ha: P < 0.80

Estimated p = 76 / 99 = 0.7677

Variance of proportion = p*(1-p)/n
= 0.8(0.2)/99 = 0.001616
S.D. of p is sqrt[0.001616] = 0.0402

b) test statistic, z = ( 0.7677 - 0.8 ) / 0.0402 = - 0.8035

P-value = P( z < - 0.8035):

The P-Value is 0.210698.

c) Since the p-value is greater than 0.01, we do not reject the null hypothesis. Based on the results there is no evidence that polygraph test results should be prohibited as evidence in trials.

d) 0.01

e) Based on the results there is no evidence that polygraph test results should be prohibited as evidence in trials.

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