A sample of size n=70 is drawn from a normal population whose standard deviation is σ=5.1 . The sample mean is x=35.46 (a) Construct a 98% confidence interval for μ. Round the answer to at least two decimal places. (b) If the population were not approximately normal, would the confidence interval constructed in part (a) be valid?Explain.

We consider the differences between the reading and writing scores of a random sample of 200 students who took the High School and Beyond Survey. The mean and standard deviation of the differences are Xread = -0.531 and 8.858 points. write (a) Calculate a 95% confidence interval for the average difference between the reading and writing scores of all students. (Round your answers to two decimal places.) (b) Interpret this interval in context. (Round your answers to two decimal places.) We are 95% confident that on the reading test students score, on average, points lower to You may need to use the appropriate table in the Appendix of Tables to answer this question. points higher than they do on the writing test. (c) Does the confidence interval provide convincing evidence that there is a real difference in the average scores? Explain. Since 0 is included in the interval, the confidence interval does not provide convincing evidence that there is a real difference in the average scores.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = Assume that o is known to be $1.92 per 100 pounds. $6.88 per 100 pounds of watermelon. (a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop (in dollars). What is the margin of error (in dollars)? (For each answer, enter a number. Round your answers to two decimal places.) lower limit $ upper limit 2$ margin of error $ (b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.27 for the mean price per 100 pounds of watermelon. (Enter a number. Round up to the nearest whole number.) farming regions (c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop (in dollars). What is the margin of error (in dollars)? Hint: 1 ton is 2000 pounds. (For each…

A sample of 14 male college students consumes an average of 14.3 gallons of beer per month, with a sample standard deviation of 5.2 gallons. You can safely assume that the population of monthly beer consumption is Normally distributed. What is the margin of error for a 90% Confidence Interval for the mean? (Leave your answer to two decimal places, ex: 18.12)