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6. The standard deviation of test scores on a certain achievement test is 11.5. A random sample of 90 scores on this test had a mean of 75.3. Based on this sample, find a 90% confidence interval for the true mean of all scores. Then give its lower limit and upper limit.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)Lower limit:Upper limit:   7. A psychologist is studying the self image of smokers, which she measures by the self-image (SI) score from a personality inventory. She would like to estimate the mean SI score, ?, for the population of all smokers. She plans to take a random sample of SI scores for smokers and estimate ? via this sample. Assuming that the standard deviation of SI scores for the population of all smokers is 90, what is the minimum sample size needed for the psychologist to be 99% confident that her estimate is within 10 of ??Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).(If necessary, consult a list of formulas.)   

8. Do pregnant women give birth the week of their due date? A study claims that 12% of the population of all pregnant women actually gave birth the week of their due date. You are a researcher who wants to test this claim, so you will select a random sample of 60 women who have recently given birth.Follow the steps below to construct a 95% confidence interval for the population proportion of all pregnant women who gave birth the week of their due date. Then state whether the confidence interval you construct contradicts the study’s claim. (If necessary, consult a list of formulas.)(a)Click on “Take Sample” to see the results from the random sample.  Take SampleNumberProportionGave birth the week of due dateDid not give birth the week of due dateEnter the values of the sample size, the point estimate of the population proportion, and the critical value you need for your 95% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select “Compute”.Critical values=z0.0052.576=z0.0102.326=z0.0251.960=z0.0501.645=z0.1001.282Sample size: Point estimate: Critical value: ComputeStandard error: Margin of error: 95% confidence interval:     (b)Based on your sample, graph the 95% confidence interval for the population proportion of all pregnant women who gave birth the week of their due date.

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