Assume that a simple random sample has been selected from a normally distributed population and test the 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 cigarette is measured. The sample has a mean of 19.6mg and a standard deviation of 3.43mg. 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 filters?

A. what are the hypotheses?

B. Identify the test statistic. T= (Round to three decimal places as needed.)

Identify the P-value.The P-value is ? (Round to four decimal places as needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Failtoreject H0. There is insufficientevidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C. Reject H0. There is insufficientevidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D. Failtoreject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

What do the results suggest, if anything, about the effectiveness of the filters?A.The results do not suggest donotsuggest that the filters are effective. B. The results suggest that the filters are effective. C. The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes. D. The results suggest that the filters increase the tar content. E.The results are inconclusive because the sample size is less than 30

Question 2

Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of people, the linear correlation coefficient is 0.930 and the equation of the regression line is y=5.88+1.08x, where x represents the IQ score of the twin born second twinbornsecond. Also, the 20 x values have a mean of 100.55 and the 20 y values have a mean of 102.9. What is the best predicted IQ of the twin born first twinbornfirst, given that the twin born second twinbornsecond has an IQ of 104? Use a significance level of 0.05

The best predicted IQ of the twin born first twinbornfirst is ? (Round to two decimal places as needed.)