IS Exam 2

19) It is desired to estimate the average total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct? A) In the population of Service industry CEOs, 97% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180. B) We are 97% confident that the average total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180. C) 97% of the sampled total compensation values fell between $2,181,260 and $5,836,180. D) We are 97% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180.

19) B

2) The Central Limit Theorem is important in statistics because A) for any sized sample, it says the sampling distribution of the sample mean is approximately normal. B) for a large n, it says the population is approximately normal. C) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. D) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.

2) D

20) When determining the sample size necessary for estimating the true population mean, which factor is NOT considered when sampling with replacement? A) the population size B) the level of confidence desired in the estimate C) the population standard deviation D) the allowable or tolerable sampling error

20) A

21) Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width? A) increase the sample size B) increase the confidence level and decrease the sample size C) decrease the confidence level D) increase the sample size and decrease the confidence level

21) D

22) In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a __________ interval. A) narrower B) less significant C) biased D) wider

22) A

11) The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample of 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or larger? A) 0.0001 B) 0.4987 C) 0.0013 D) 0.0228

11) D

43) How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct? A) At α = 0.05, there is sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues. B) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is 60 tissues. C) At α = 0.10, there is sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues. D) At α = 0.05, there is not sufficient evidence to conclude that the average number of tissues used during a cold is not 60 tissues.

43) C & B too

6) A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) __________ sample.

6) biased

10) The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and a standard deviation of 0.8 pounds. If a sample of 16 fish is taken, what would the standard error of the mean weight equal? A) 0.200 B) 0.003 C) 0.050 D) 0.800

10) A

12) The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would A) increase the sample size to 400.B) decrease the sample size to 50. C) increase the sample size to 200. D) decrease the sample to 25.

12) A

13) Which of the following is true regarding the sampling distribution of the mean for a large sample size? A) It has the same shape, mean, and standard deviation as the population. B) It has a normal distribution with the same mean as the population but with a smaller standard deviation. C) It has the same shape and mean as the population, but has a smaller standard deviation. D) It has a normal distribution with the same mean and standard deviation as the population.

13) B

15) True or False: Suppose μ = 50 and σ2 = 100 for a population. In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51. A) True B) False

15) B

16) The width of a confidence interval estimate for a proportion mean will be A) narrower for 90% confidence than for 95% confidence. B) wider for a sample size of 100 than for a sample size of 50. C) narrower when the sample proportion is 0.50 than when the sample proportion is 0.20. D) narrower for 99% confidence than for 95% confidence.

16) A

17) If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25, where the standard deviation of the sample s = 0.05, the critical value of t will be A) 2.7874 B) 2.7970 C) 2.4851 D) 2.4922

17) B

18) The t distribution A) has more area in the tails than does the standard normal distribution. B) assumes the population is normally distributed. C) approaches the normal distribution as the sample size increases. D) all of the above

18) D

23) A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X (line over it) = $50.50 and s2 = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ? A) a t distribution with 14 degrees of freedom B) a t distribution with 15 degrees of freedom C) approximately normal with a mean of $50.50 D) a standard normal distribution

23) A

30) True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7, a 90% confidence interval will have a width of 2.36. A) True B) False

30) B

38) If the Type I error (α) for a given test is to be decreased, then for a fixed sample size n A) the Type II error (β) will increase.B) the power of the test will increase. C) a one-tailed test must be utilized. D) the Type II error (β) will also decrease.

38) A

39) The power of a statistical test is A) the probability of not rejecting H0 when it is false. B) the probability of rejecting H0 when it is false. C) the probability of not rejecting H0 when it is true. D) the probability of rejecting H0 when it is true.

39) B

4) Which of the following statements about the sampling distribution of the sample mean is INCORRECT? A) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. B) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n ≥ 30). C) The standard deviation of the sampling distribution of the sample mean is equal to σ. D) The mean of the sampling distribution of the sample mean is equal to μ.

4) C

44) If, as a result of a hypothesis test, we reject the null hypothesis when it is false, then we have committed A) a Type II error. B) an acceptance error. C) no error. D) a Type I error.

44) C

1) Sampling distributions describe the distribution of A) parameters. B) statistics. C) both parameters and statistics. D) neither parameters nor statistics.

1) B

14) True or False: Suppose μ = 50 and σ2 = 100 for a population. In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96. A) True B) False

14) A

24) Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield = 180.975 and s = 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States, assuming a normal distribution for the endowments. A) $180.975 ± $99.123 B) $180.975 ± $94.066 C) $180.975 ± $119.605 D) $180.975 ± $116.621

24) C

25) A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Presently the students pay $55 per credit hour. The university system administrators are contemplating charging each student a set fee of $750 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a sample would they need to take?

25) n = 2033

26) An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval? A) $728.60 B) $232.60 C) $465.23 D) $364.30

26) C

27) The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress? A) 740 B) 920 C) 1,660 D) 830

27) D

28) The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate? A) 125 B) 13 C) 4 D) 11

28) D

29) True or False: A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 4.52 seconds to 5.18 seconds. A) True B) False

29) B

3) For air travelers, one of the biggest complaints involves the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a skewed-right distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. A) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. B) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. C) Distribution is skewed-right with mean = 10 minutes and standard error = 0.8 minutes. D) Distribution is skewed-right with mean = 10 minutes and standard error = 8 minutes.

3) A

31) Which of the following would be an appropriate null hypothesis? A) The mean of a population is greater than 55. B) The mean of a population is equal to 55. C) The mean of a sample is equal to 55. D) Only A and C are true.

31) B

32) Which of the following would be an appropriate alternative hypothesis? A) The mean of a sample is equal to 55. B) The mean of a population is equal to 55. C) The mean of a population is greater than 55. D) The mean of a sample is greater than 55.

32) C

33) A Type I error is committed when A) we don't reject a null hypothesis that is true. B) we reject a null hypothesis that is true. C) we don't reject a null hypothesis that is false. D) we reject a null hypothesis that is false.

33) B

34) The power of a test is measured by its capability of A) rejecting a null hypothesis that is true. B) not rejecting a null hypothesis that is false. C) not rejecting a null hypothesis that is true. D) rejecting a null hypothesis that is false.

34) D

35) True or False: For a given level of significance, if the sample size is increased, the probability of committing a Type II error will increase. A) True B) False

35) B

36) If an economist wishes to determine whether there is evidence that average family income in a community exceeds $25,000 A) a one-tailed test should be utilized. B) either a one-tailed or two-tailed test could be used with equivalent results. C) a two-tailed test should be utilized. D) none of the above

36) A

37) If an economist wishes to determine whether there is evidence that average family income in a community equals $25,000 A) a two-tailed test should be utilized. B) a one-tailed test should be utilized. C) either a one-tailed or two-tailed test could be used with equivalent results. D) none of the above

37) A

40) How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60. A) H0 : ≥ 60 and H1 : < 60 B) H0 : μ ≤ 60 and H1 : μ > 60 C) H0 : μ ≥ 60 and H1 : μ < 60 D) H0 : = 52 and H1 : ≠ 52

40 C

41) How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Using the sample information provided, calculate the value of the test statistic. A) t = (52 - 60)/22 B) t = (52 - 60)/(22/1002) C) t = (52 - 60)/(22/100) D) t = (52 - 60)/(22/10)

41) A

42) How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, s = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct? A) At α = 0.05, we do not reject H0. B) At α = 0.05, we accept H0. C) At α = 0.10, we do not reject H0. D) At α = 0.05, we reject H0.

42) D

5) Suppose the ages of students in Statistics 101 follow a skewed-right distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is INCORRECT? A) The standard deviation of the sample mean is equal to 3 years. B) The mean of the sample mean is equal to 23 years. C) The standard error of the sample mean is equal to 0.3 years. D) The shape of the sampling distribution is approximately normal.

5) A

7) Suppose a sample of n = 50 items is drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a probability distribution with μ = 6 ounces and σ = 2.5 ounces. Which of the following is true about the sampling distribution of the sample mean if a sample of size 15 is selected? A) The mean of the sampling distribution is 6 ounces. B) The shape of the sample distribution is approximately normal. C) The standard deviation of the sampling distribution is 2.5 ounces. D) All of the above are correct.

7) A

8) Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. Suppose a sample of 100 major league players was taken. Find the approximate probability that the average salary of the 100 players exceeded $1 million. A) Approximately 1 B) 0.2357 C) 0.7357 D) approximately 0

8) A

9) At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeters. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

9) 0.2710