Assume that the normal distribution

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12. Assume that the normal distribution applies and find the critical z value(s).
A = 0.04; H1 is u not equal to 98.6 F z= (round to two decimal places)
14. Find the value of the test statistic z using = p (with hat) – p (numerator) (denominator) is the square root pq/n
The claim is that the proportion of Ps with yellow pods is equal to 0.25(or 25%). The sample statistics from one experiment include 430 peas with 125 of them having yellow pods.
Z = (round to two decimals)
16. Trials in an experiment with a polygraph includes 97 results that includes 22 cases of wrong results and 75 cases of correct results. Use a 0.05 significant level to test the claim that such polygraph results are correct less than 80% of the time. Identify the null hypothesis, alternative hypothesis, test statistic, P- value, conclusion about the null hypothesis, and finally conclusion that addresses the original claim. Use the P- value method. Use the normal distribution as an approximation of the binomial distribution (please answer all parts clearly).
17. Assume that a simple random sample has been selected from a normally distribution population and the test given claim. Identify the null and alternative hypotheses, test statistic, P – value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarettes is measured. The sample has a mean of 19.4 mg and SD of 3.38 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filter? (please answer all parts clearly).
18. The heights were measured for nine super models. They have a mean of 64.8 inches and SD of 2.4 inches. Use the traditional method and a 0.01 significant level to test the claim that super models have height with a mean that is greater than the mean of 63.6 inches for women from the general population. (please have answer inclusive of rejection or failure to reject because of a greater than or not greater than critical value).