**Problem 1**

For a simple random sample, n = 700 and p = 0.63. At the 0.025 level, test H0: ≤ 0.60 versus

H1: > 0.60 by answering the following questions:

Please round your answer to 2 decimal places

a. The test statistic is .

b. The critical value is

Problem 2

The director of admissions at a large university says that 15% of high school juniors to whom she sends university literature eventually apply for admission. In a sample of 300 persons to whom materials were sent, 30 students applied for admission. In a two-tail test at the 0.05 level of significance, answering the following questions to determine whether we should reject the director’s claim:

Please round your answer to 2 decimal places

a. The critical values are +/-

Problem 3

For a simple random sample, n = 200 p = 0.34. At the 0.01 level, test H0: pi = 0.40 versus H1: pi ≠ 0.40 by answering the following questions:

Please round your answer to 2 decimal places

a. The test statistic is .

b. The critical values are +/-

Problem 4

For a sample of 35 items from a population for which the standard deviation is = 20.5, the sample mean is 458.0.

Please round your answers to 2 decimal places.

a. The lower bound of the 95% confidence interval for the population mean is

Problem 5

Following maintenance and calibration, an extrusion machine produces aluminum tubing with a mean outside diameter of 2.500 inches, with a standard deviation of 0.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accumulated deposits and mechanical wear causes the mean diameter to “drift” away from the desired 2.500 inches. For a recent random sample of 34 tubes, the mean diameter was 2.509 inches.

Please round your answer to 3 decimal places.

a. The lower bound of the 99% confidence interval for the population mean is .

b. The upper bound of the 99% confidence interval for the population mean is