Directions:Show all work including formulas employed.Include a concluding statement to answer the question.A sketch must accompany the solutions for question 3.

1.Assume that body temperatures of healthy adults are normally distributed with a mean of 98.2F and a standard deviation of 0.62F.Suppose you collect a sample of size n healthy adults.Would you be more likely to obtain a sample mean of 97.9 or less if n = 25 or if n = 100?Explain.

2.How much do Americans sleep each night?Based on a random sample of 1120 Americans 15 years of age or older, the mean amount of sleep per night is 8.17 according to the American Time Use Survey conducted by the Bureau of Labor Statistics.Assuming the population standard deviation for amount of sleep per night is 1.2 hours, construct and interpret a 95% confidence interval for the mean amount of sleep per night of Americans 15 years of age or older.

3.According to the U.S. Department of Agriculture, the mean calorie intake of males 20 to 39 years old is 2716 with a standard deviation of 72.8.

a)What is the probability in a random sample of 35 males between the ages of 20 and 39 would result in a sample mean of 2750 calories or higher?

b)Would you consider it unusual to have a sample mean of 2750 or higher for a sample size of 35?Explain.

4.Explain the difference between a point estimate and a confidence interval estimate.

5.In a random sample of 20 boxes of cereal, the mean sodium content is 173.1 mg with a standard deviation of 43 mg.Assume the sodium content of cereals is normally distributed.

a)State a point estimate for the true mean sodium content of cereals.

b)Construct a 90% confidence interval estimate for the true value of sodium in cereal. Interpret the interval estimate.

6.The Harvard School of Public Health conducted a survey of 2770 adults in the United States to determine the proportion of Americans who own guns.According to the results, Injury Prevention in 2007 reported that 26% of adults own at least one gun.State and estimate the population parameter using both a point estimate and a 99% confidence interval estimate.

7.In an October 2003 poll conducted by the Gallup Organization, 684 of 1006 randomly selected adults aged 18 years old or older stated they think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother.

a.Obtain a point estimate for the proportion of adults aged 18 or older who think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother.

b.Construct a 95% confidence interval for the proportion of adults aged 18 or older who think the government should make partial birth abortions illegal, except in cases necessary to save the life of the mother.Interpret the interval.

8.Are boys more likely?A random sample of 24,468 records of newborn firstborn children revealed the number of boys in the sample to be 13,175 boys.Provide a point estimate and 98% confidence interval estimate for the true proportion of newborn baby boys.Interpret the interval.

9.In January 2007 Consumer, Reports published a study of bacterial contamination of chicken sold in the United States.They purchased 525 broiler chickens from various stores in 23 states and tested them for bacterial contamination.Lab tests indicated 83% of the chickens were contaminated with Campylobacter.

How would you justify a claim by the USDA that the number of chickens tested was not large enough since 9 billion chickens are sold each year in the U.S.?