Name______________________________ QAS 228-001

Professor T. Miller-Greaves December 5, 13

Examination #4 – Fall 2013

Directions: Read and complete each question provided in this exam. Each

correct answer will be worth 5 points. Please include your answers directly in

your email and not as an attachment. Partial credit will only be given to problems

that require a particular formula and computation. Upon completion of this exam,

return the answers only to me via email to prof.tmillergreaves@me.com and

Tarshene.miller-greaves@liu.edu by Sunday, December 8, 2013 at 5:00pm. In the

subject of your email, please be sure to include your name and Exam #4 and QAS

228-002. Should you have any questions, you can contact me at 718-781-6446

and leave a voicemail message or send me a text message. Thank you.

PART I – MULTIPLE CHOICE – Choose the correct answer from the four choice

answers. Each correct answer will be worth 5 points.

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

Answer _______ 2. The Central Limit Theorem is important in statistics because

A) for a large n, it says the population is approximately normal. B) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. C) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. D) for any sized sample, it says the sampling distribution of the sample mean is approximately normal.

Answer _______ 3. For air travelers, one of the biggest complaints is of 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 right skewed 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 right skewed with mean = 10 minutes and standard error = 0.8 minutes. B) Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes. C) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. D) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes.

Answer _______ 4. Which of the following is true about the sampling distribution of the sample mean?

A) The mean of the sampling distribution is always μ. B) The standard deviation of the sampling distribution is always σ. C) The shape of the sampling distribution is always approximately normal. D) All of the above are true.

Answer _______ 5. Suppose the ages of students in Statistics 101 follow a right skewed 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 mean of the sampling distribution is equal to 23 years. B) The standard deviation of the sampling distribution is equal to 3 years. C) The shape of the sampling distribution is approximately normal. D) The standard error of the sampling distribution is equal to 0.3 years.

Answer _______ 6. Suppose a sample of n = 50 items is selected 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 standard deviation of the sampling distribution is 2.5 ounces. C) The shape of the sampling distribution is approximately normal. D) All of the above are correct.

Answer _______

7. Suppose a 95% confidence interval for μ has been constructed. If it is decided to

take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would ________. (Assume that the sample statistics gathered would not change very much for the new sample.) A) be larger than the current interval width B) be narrower than the current interval width C) be the same as the current interval width D) be unknown until actual sample sizes and reliability levels were determined

Answer _______ 8. A 99% confidence interval estimate can be interpreted to mean that

A) if all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. B) we have 99% confidence that we have selected a sample whose interval does include the population mean. C) Both of the above. D) None of the above.

Answer _______ 9. An economist is interested in studying the incomes of consumers in a particular

country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the width of the 90% confidence interval? A) $232.60 B) $364.30 C) $465.23 D) $728.60

Answer _______

10. 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) 2.7969. B) 2.7874. C) 2.4922. D) 2.4851.

Answer _______

11. The standard error of the population proportion will become larger

A) as population proportion approaches 0. B) as population proportion approaches 0.50. C) as population proportion approaches 1.00. D) as the sample size increases.

Answer _______ 12. A major department store chain is interested in estimating the mean 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 = $50.50 and S = 20. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution. A) $50.50 ± $9.09 B) $50.50 ± $10.12 C) $50.50 ± $11.00 D) $50.50 ± $11.08

Answer _______ PART II – FILL IN THE BLANK– Provide the blank space with the correct answer. 13. The amount of tea leaves in a can from a particular production line is normally

distributed with μ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 100 grams?

Answer _______ 14. A prison official wants to estimate the proportion of cases of recidivism. Examining

the records of 250 convicts, the official determines that there are 65 cases of recidivism. A confidence interval will be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated standard error of the sample proportion. For this sample, the estimated standard error is ________.

Answer _______

PART III – MULTIPLE CHOICE – Choose the correct answer from the four choice

answers. Each correct answer will be worth 5 points.

15. Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference. A) In repeated sampling, the population parameter would fall in the given interval 95% of the time. B) In repeated sampling, 95% of the intervals constructed would contain the population mean. C) 95% of the observations in the entire population fall in the given interval. D) 95% of the observations in the sample fall in the given interval.

Answer _______ 16. As an aid to the establishment of personnel requirements, the director of a hospital

wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X = 19.8 and S = 5. Which of the following assumptions is necessary in order for a confidence interval to be valid? A) The population sampled from has an approximate normal distribution. B) The population sampled from has an approximate t distribution. C) The mean of the sample equals the mean of the population. D) None of these assumptions are necessary.

Answer _______

17. A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 95% confidence interval for π is 0.59 ± 0.07. Interpret this interval. A) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66. B) 95% of the students get between 52% and 66% of their tuition paid for by financial aid. C) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid. D) We are 95% confident that 59% of the students are on some sort of financial aid.

Answer _______ 18. When determining the sample size for a proportion for a given level of confidence

and sampling error, the closer to 0.50 that π is estimated to be, the sample size

required ________. A) is smaller B) is larger C) is not affected D) can be smaller, larger or unaffected

Answer _______ 19. 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 population standard deviation C) The level of confidence desired in the estimate D) The allowable or tolerable sampling error

Answer _______ 20. 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) 11 D) 4

Answer _______

PART IV. Extra Credit Questions. Each correct answer is worth 2 points. 21. It is desired to estimate the mean total compensation of CEOs in the Service

industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct? A) 95% of the sampled total compensation values fell between $2,181,260 and $5,836,180. B) We are 95% confident that the mean of the sampled CEOs falls in the interval $2,181,260 to $5,836,180. C) In the population of Service industry CEOs, 95% of them will have total compensations that fall in the interval $2,181,260 to $5,836,180. D) We are 95% confident that the mean total compensation of all CEOs in the

Service industry falls in the interval $2,181,260 to $5,836,180. Answer _______ TABLE A The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours. A random sample of 64 of these light bulbs is taken. 22. Referring to Table A, what is the probability that the sample mean lifetime is more

than 1,550 hours? Answer _______ 23. Referring to Table A, the probability is 0.15 that the sample mean lifetime is more

than how many hours? Answer _______ 24. Referring to Table A, the probability is 0.20 that the sample mean lifetime differs

from the population mean lifetime by at least how many hours? Answer _______ 25. For sample sizes greater than 30, the sampling distribution of the mean will be

approximately normally distributed A) regardless of the shape of the population. B) only if the shape of the population is symmetrical. C) only if the standard deviation of the samples are known. D) only if the population is normally distributed. Answer _______