Posted: May 8th, 2021

Question 1

Let x be a random variable representing the SAT math score of student. We may assume that x has a normal distribution and that the population standard deviation is 25. A large university claims the average SAT math score for incoming freshman is 650. You suspect that this claim is too high and decide to test the claim. You select a random sample of 75 incoming freshman and find the sample mean SAT math score to be 645. If you assume that the population mean is 650, find the P-value corresponding to the hypothesis that the average SAT score is less than 650 (i.e. left-tail test).

Answer

A. 0.037

B. 0.061

C. 0.042

D. 0.053

Question 2

A random sample of 10 mathematics dictionaries had an average price of $17.50 with a sample standard deviation of $3.85. Find the 95% confidence interval for µ, the population mean price of all mathematics dictionaries.

Answer A. (14.64, 20.36)

B. (14.98, 20.02)

C. (14.34, 20.66)

D. (14.75, 20.25)

Question 3

In a survey of 900 adults, 240 said that they watched the World Cup final on television. Using these sample statistics, calculate the margin of error, E, for a 90% confidence interval for the proportion of all adults that watched the World Cup final on television.

Answer

A. 0.019

B. 0.024

C. 0.029

D. 0.034

Question 4

Let x be a random variable representing the length of a cutthroat trout in Pyramid lake. A friend claims that the average length of trout caught in this lake is 19 inches. To test this claim we find that a sample of 13 trout has a mean length of 18.1 inches with a sample standard deviation of 3.3 inches. The population standard deviation is unknown. If you assume that the population mean is 19, find the P-value corresponding to the hypothesis that the average cutthroat trout length is different from 19 (i.e. two-tail test).

Answer

A. 0.295

B. 0.324

C. 0.162

D. 0.344

Question 5

In a certain region, the mean annual salary for plumbers is $51,000. Let x be a random variable that represents a plumber’s salary. Assume the standard deviation is $1300. If a random sample of 100 plumbers is selected, what is the probability that the sample mean is greater than $51,300?

Answer A. 0.32

B. 0.03

C. 0.41

D. 0.01

Question 6

Find the critical value tc for a 95% confidence level when the sample size is 18. Use Table 4 on page A10 (Appendix)

Answer A. 1.740

B. 2.110

C. 2.101

D. 1.734

Question 7

The lengths of Atlantic croaker fish are normally distributed, with a mean of 10 inches and a standard deviation of 2 inches. Let x be a random variable that represents the length of an Atlantic croaker fish. Suppose an Atlantic croaker fish is randomly selected. Find the probability that length of the fish is between 8.5 inches and 10.5 inches.

Answer A. 0.63

B. 0.54

C. 0.37

D. 0.77

Question 8

Let x be a random variable representing the SAT math score of student. We may assume that x has a normal distribution and that the population standard deviation is 25. A large university claims the average SAT math score for incoming freshman is 650. You suspect that this claim is too high and decide to test the claim. You select a random sample of 75 incoming freshman and find the mean SAT math score to be 645. If you assume that the population mean is 650, find the standardized test statistic based on the sample.

Answer A. -1.65

B. -1.73

C. 1.73

D. 1.65

Question 9

Let x be a random variable representing the length of a cutthroat trout in Pyramid lake. A friend claims that the average length of trout caught in this lake is 19 inches. To test this claim we find that a sample of 13 trout has a mean length of 18.1 inches with a sample standard deviation of 3.3 inches. The population standard deviation is unknown. If you assume that the population mean is 19, find the standardized test statistic based on the sample.

Answer A. -0.914

B. -0.983

C. -1.215

D. .1.021

Question 10

Find the area below the standard normal curve to the right of z = 2.

Answer

A. 0.011

B. 0.022

C. 0.978

D. 0.489

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