1. Consider a normal population with µ = 25 and σ = 7.0.
(A) Calculate the standard score for a value x of 27.
(B) Calculate the standard score for a randomly selected sample of 45 -with
x = 27. The sign is on x please am unable to copy it right.
(C) Explain why the standard scores of 27 are different between A and B above.
2. Assume that the mean SAT score in Mathematics for 11th graders across the nation is 500, and that the standard deviation is 100 points. Find the probability that the mean SAT score for a randomly selected group of 150 11th graders is between 485 and 515.
3. Assume that a sample is drawn and z(α/2) = 1.65 and σ = 30. Answer the following questions:
(A)If the Maximum Error of Estimate is 0.04 for this sample, what would be the sample size?
(B)Given that the sample Size is 400 with this same z(α/2) and σ, what would be the Maximum Error of Estimate?
(C)What happens to the Maximum Error of Estimate as the sample size gets larger?
(D)What effect does the answer to C above have to the size of the confidence interval?
4. By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the standard deviation is 3.22 seconds.
Answer each of the following (show all work):
(A) How many measurements should be made in order to be 98% certain that the maximum error of estimation will not exceed 0.5 seconds?
(B) What sample size is required for a maximum error of 1.5 seconds?
5. A 95% confidence interval estimate for a population mean was computed to be (43.3, 60.1). Determine the mean of the sample, which was used to determine the interval estimate (show all work).
6. A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having two children. A sample of 120 was taken, and the mean amount spent was $195.37. Assuming a standard deviation equal to $37.87, find the 90% confidence interval for m, the mean for all such families (show all work).
7. A confidence interval estimate for the population mean is given to be (41.16, 49.85). If the standard deviation is 16.290 and the sample size is 54, answer each of the following (show all work):
(A) Determine the maximum error of the estimate, E.
(B) Determine the confidence level used for the given confidence interval.
8. Write a correct null and alternative hypothesis for testing the claim that the mean life of a battery for a cell phone is at least 80 hours.