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Question and answer key to exercise drills (chapter 7-9)...

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MGTS 103

Ch 7 Test your knowledge

1. Parameters are a. numerical characteristics of a sample. b. numerical characteristics of a population. c. the averages taken from a sample. d. numerical characteristics of either a sample or a population. ANSWER: b 2. How many simple random samples of size 3 can be selected from a population of size 8? a. 336 b. 24 c. 56 d. 6561 ANSWER: c 3. Sampling distribution of is the a. probability distribution of the sample mean. b. probability distribution of the sample proportion. c. mean of the sample. d. mean of the population. ANSWER: a 4. A simple random sample of 100 observations was taken from a large population. The sample mean and the standard deviation were determined to be 50 and 5, respectively. The standard error of the mean is a. 0.5. b. 2. c. 5. d. 10. ANSWER: a 5. A population has a standard deviation of 16. If a sample of size 64 is selected from this population, what is the probability that the sample mean will be within ±2 of the population mean? a. 0.6826 b. 0.3413 c. -0.6826 d. Since the mean is not given, there is no answer to this question. ANSWER: a 6. The probability distribution of all possible values of the sample proportion a. probability density function of . b. sampling distribution of .

is the

c. same as , since it considers all possible values of the sample proportion. d. sampling distribution of . ANSWER: d 7. In computing the standard error of the mean, the finite population correction factor is used when a. N/n > 0.05. b. N/n 0.05. c. n/N > 0.05. d. n/N 30. ANSWER: c 8. A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is a. 0.100. b. 0.010. c. 0.001. d. 0.002. ANSWER: d 9. The closer the sample mean is to the population mean, a. the larger the sampling error. b. the smaller the sampling error. c. the sampling error equals 1. d. none of these alternatives is correct. ANSWER: b 10. As the sample size increases, the a. standard deviation of the population decreases. b. population mean increases. c. standard error of the mean decreases. d. standard error of the mean increases. ANSWER: c 11. A simple random sample from an infinite population is a sample selected such that a. each element is selected independently and from the same population. b. each element has a 0.5 probability of being selected. c. each element has a probability of at least 0.5 of being selected. d. the probability of being selected changes. ANSWER: a

12. In point estimation a. data from the population is used to estimate the population parameter. b. data from the sample is used to estimate the population parameter. c. data from the sample is used to estimate the sample statistic. d. the mean of the population equals the mean of the sample. ANSWER: b 13. The sample statistic s is the point estimator of a. μ . b. σ . c. . d. . ANSWER: b 14. The sample mean is the point estimator of a. μ. b. σ. c. . d. . ANSWER: a 15. If we consider the simple random sampling process as an experiment, the sample mean is a. always zero. b. always smaller than the population mean. c. a random variable. d. exactly equal to the population mean. ANSWER: c 16. As the sample size becomes larger, the sampling distribution of the sample mean approaches a _____ distribution. a. Binomial b. Poisson c. Normal d. Chi-square ANSWER: c 17. Whenever the population has a normal probability distribution, the sampling distribution of normal probability distribution for a. large sample sizes.

is a

b. small sample sizes. c. any sample size. d. samples of size thirty or greater. ANSWER: c 18. The sampling error is the a. same as the standard error of the mean. b. difference between the value of the sample mean and the value of the population mean. c. error caused by selecting a bad sample. d. standard deviation multiplied by the sample size. ANSWER: b 19. From a population of 200 elements, a sample of 49 elements is selected. It is determined that the sample mean is 56 and the sample standard deviation is 14. The standard error of the mean is a. 3. b. 2. c. greater than 2. d. less than 2. ANSWER: d 20. Which of the following is(are) point estimator(s)? a. σ b. μ c. s d. α ANSWER: c 21. A probability distribution of all possible values of a sample statistic is known as a. a sample statistic. b. a parameter. c. simple random sampling. d. a sampling distribution. ANSWER: d 22. The standard deviation of a point estimator is called the a. standard deviation. b. standard error. c. point estimator. d. variance of estimation. ANSWER: b 23. The sample statistic, such as , s, or known as a a. point estimator.

, that provides the point estimate of the population parameter is

b. parameter. c. population parameter. d. population statistic. ANSWER: a 24. The purpose of statistical inference is to provide information about the a. sample based upon information contained in the population. b. population based upon information contained in the sample. c. population based upon information contained in the population. d. mean of the sample based upon the mean of the population. ANSWER: b 25. Random samples of size 600 are taken from an infinite population whose population proportion is 0.4. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is a. 0.0004. b. 0.2400. c. 0.4000. d. 0.0200. ANSWER: d 26. A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have _____ of being selected. a. the same probability b. a probability of 1/n c. a probability of 1/N d. a probability of N/n ANSWER: a 27. A sample of 92 observations is taken from an infinite population. The sampling distribution of approximately a. normal because is always approximately normally distributed.

is

b. normal because the sample size is small in comparison to the population size. c. normal because of the central limit theorem. d. none of these alternatives is correct. ANSWER: c 28. Random samples of size 400 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are a. 0.2 and .04. b. 0.2 and 0.02. c. 20 and .04. d. 20 and 0.02.

ANSWER: b 29. A sample of 25 observations is taken from an infinite population. The sampling distribution of a. not normal since n < 30. b. approximately normal because is always normally

is

distributed. c. approximately normal if np 5 and n(1-P) 5. d. approximately normal if np > 30 and n(1-P) > 30. ANSWER: c 30. A finite population correction factor is needed in computing the standard deviation of the sampling distribution of sample means a. whenever the population is infinite. b. whenever the sample size is more than 5% of the population size. c. whenever the sample size is less than 5% of the population size. d. irrespective of the size of the sample. ANSWER: b 31. Doubling the size of the sample will a. reduce the standard error of the mean to one-half its current value. b. reduce the standard error of the mean to approximately 70% of its current value. c. have no effect on the standard error of the mean. d. double the standard error of the mean. ANSWER: b 32. Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is a. 300. b. approximately 300. c. 0.75. d. 0.25. ANSWER: c 33. The standard deviation of a. standard b. sample mean c. deviated d. standard error of the ANSWER: d

is referred to as the _____ proportion.

34. The value of the _____ is used to estimate the value of the population parameter

a. population statistic b. sample parameter c. population estimate d. sample statistic ANSWER: d 35. The population being studied is usually considered _____ if it involves an ongoing process that makes listing or counting every element in the population impossible. a. finite b. infinite c. skewed d. symmetric ANSWER: b 36. The standard error of the proportion will become larger as a. n increases. b. p approaches 0. c. p approaches .5. d. p approaches 1. ANSWER: c 37. All of the following are true about the standard error of the mean except a. it is larger than the standard deviation of the population. b. it decreases as the sample size increases. c. its value is influenced by the standard deviation of the population. d. it measures the variability in sample means. ANSWER: a 38. The extent of the sampling error might be affected by all of the following factors except the a. variability of the population. b. expected value of the sample statistic c. sample size. d. sampling method used. ANSWER: b 39. The desired situation is when the sampled population is _____ the targeted population. a. identical to b. larger than c. smaller than d. more varied than ANSWER: a 103

Ch 8 Discussion - Test Your Knowledge

Student: __________

1. In interval estimation, as the sample size becomes larger, the interval estimate a. becomes narrower. b. becomes wider. c. remains the same, because the mean is not changing. d. gets closer to 1.96. a

2. In an interval estimation for a proportion of a population, the value of z at 99.2% confidence is a. 2.65. b. 2.41. c. 1.96. d. 1.645. a

3. When s is used to estimate σ, the margin of error is computed by using the a. normal distribution. b. t distribution. c. mean of the sample. d. mean of the population. b

4. In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 58 items is selected. The mean of the sample is determined to be 36. The associated number of degrees of freedom for reading the t value is a. 35. b. 36. c. 57. d. 58. c

5. If we want to provide a 95% confidence interval for the mean of a population, the confidence coefficient will be a. .485. b. 1.96. c. .95. d. 1.645. c

6. As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution a. becomes larger.

b. becomes smaller. c. stays the same. d. fluctuates. b

7. For the interval estimation of μwhen σis known and the sample is large, the proper distribution to use is the a. normal distribution. b. t distribution with n degrees of freedom. c. t distribution with n + 1 degrees of freedom. d. t distribution with n - 1 degrees of freedom. a

8. An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the a. confidence level. b. interval estimate. c. margin of error. d. point estimate. b

9. The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the a. confidence level. b. margin of error. c. parameter estimate. d. planning value. b

10. In interval estimation, the t distribution is applicable only when the a. population has a mean of less than 30. b. sample standard deviation is used to estimate the population standard deviation. c. variance of the population is known. d. mean of the population is unknown. b

11. In developing an interval estimate, if the population standard deviation is unknown, a. it is impossible to develop the interval estimate. b. the standard deviation is arrived at using the range. c. the sample standard deviation must be used. d. it is assumed that the population standard deviation is

1. c

12. From a population that is not normally distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (μ). a. The normal distribution can be used. b. The t distribution with 5 degrees of freedom must be used. c. The t distribution with 6 degrees of freedom must be used. d. The sample size must be increased. d

13. A sample of 200 elements from a population with a known standard deviation is selected. For an interval estimation of μ, the proper distribution to use is the a. normal distribution. b. t distribution with 200 degrees of freedom. c. t distribution with 201 degrees of freedom. d. t distribution with 199 degrees of freedom. a

14. From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the a. normal distribution. b. t distribution with 25 degrees of freedom. c. t distribution with 26 degrees of freedom. d. t distribution with 24 degrees of freedom. d

15. The t value for a 95% confidence interval estimation with 96 degrees of freedom is a. 1.661. b. 1.985. c. 1.291. d. 1.986. b

16. As the sample size increases, the margin of error a. increases. b. decreases.

c. stays the same. d. fluctuates depending on the mean. b

17. A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ a. becomes narrower. b. becomes wider. c. does not change. d. becomes 100.1 to 120.1. a

18. Using an α= .04, a confidence interval for a population proportion is determined to be .65 to .75. For the same data, if αis decreased, the confidence interval for the population proportion a. becomes narrower. b. becomes wider. c. uses a zero margin of error. d. remains the same. b 19. The ability of an interval estimate to contain the value of the population parameter is described by the a. confidence level. b. degrees of freedom. c. precise value of the population mean μ. d. point estimate. a

20. If we change a 95% confidence interval estimate to a 99% confidence interval estimate, we can expect the a. width of the confidence interval to increase. b. width of the confidence interval to decrease. c. width of the confidence interval to remain the same. d. sample size to increase. a 21. When the level of confidence decreases, the margin of error a. stays the same. b. becomes smaller. c. becomes larger. d. becomes smaller or larger, depending on the sample mean. b

22. In general, higher confidence levels provide a. wider confidence intervals. b. narrower confidence intervals. c. a smaller standard error. d. unbiased estimates. a

23. We can use the normal distribution to make confidence interval estimates for the population proportion, p, when a. np > 5. b. n(1 - p) > 5. c. p has a normal distribution. d. both np > 5 and n(1 - p) > 5. d 24. A random sample of 25 employees of a local company has been taken. A 95% confidence interval estimate for the mean systolic blood pressure for all employees of the company is 123 to 139. Which of the following statements is valid? a. 95% of the sample of employees has a systolic blood pressure between 123 and 139. b. If the sampling procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure. c. 95% of the population of employees has a systolic blood pressure between 123 and 139. d. If the sampling procedure were repeated many times, 95% of the sample means would be between 123 and 139. b

25. The t distribution should be used whenever the a. sample size is less than 30. b. sample standard deviation is used to estimate the population standard deviation. c. population is not normally distributed. d. population standard deviation is known. b

26. The mean of the t distribution is a. 0. b. .5. c. 1. d. problem specific. a

27. We can reduce the margin of error in an interval estimate of p by doing any of the following except

a. increasing the sample size. b. increasing the planning value p* to . 5. c. increasing α. d. reducing the confidence coefficient. b

28. The sample size that guarantees the estimate of a population proportion satisfying the margin of error requirement is computed using a planning value of p equal to a. .01. b. .50. c. .51. d. .99. b

29. The use of the normal probability distribution as an approximation of the sampling distribution of based on the condition that both np and n(1 - p) equal or exceed a. .05. b. 5. c. 10. d. 30.

is

b

30. To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except a. desired margin of error. b. confidence level. c. population standard deviation. d. degrees of freedom. d

31. The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the a. finite correction factor. b. sample size. c. degrees of freedom. d. standard deviation. c

32. To compute the necessary sample size for an interval estimate of a population proportion, all of the following procedures are recommended when p is unknown except a. use the sample proportion from a previous study. b. use the sample proportion from a preliminary

sample. c. use 1.0 as an estimate. d. use judgment or a best guess. c

33. To compute the necessary sample size for an interval estimate of a population mean, all of the following procedures are recommended when σ is unknown except a. use the estimated σ from a previous study. b. use the sample standard deviation from a preliminary sample. c. use judgment or a best guess. d. use .5 as an estimate. d

34. For a given confidence level and when σ is known, the margin of error in a confidence interval estimate a. varies from sample to sample of the same size. b. is the same for all samples of the same size. c. increases as the sample size increases. d. is independent of sample size. b

35. The margin of error in an interval estimate of the population mean is a function of all of the following except a. α. b. sample mean. c. sample size. d. variability of the population. b

36. As the degrees of freedom increase, the t distribution approaches the _____ distribution. a. uniform b. normal c. exponential d. P b

37. The general form of an interval estimate of a population mean or a population proportion is the _____ plus and minus the _____. a. population mean, standard error b. population proportion, standard error c. point estimate, margin of error d. planning value, confidence coefficient

c

38. The level of significance α a. can be any positive value. b. is always a negative value. c. is (1 - confidence coefficient). d. can be any value between -1.96 to 1.96. c

39. Confidence intervals for the population mean µ and population proportion p _____ as the size of the sample increases. a. become narrower b. become wider c. remain the same d. get closer to 1. a 40. Potential sampling error _____as the sample size increases. a. increases b. decreases c. stays the same d. fluctuates depending on the mean b

MGTS 103

Ch 9 Drill – Test Your Knowledge

1. The critical value of t for a two-tailed test with 10 degrees of freedom using α = .05 is a. 1.833. b. 1.812. c. 2.262. d. 2.228. ANSWER: d 2. What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one-tailed or two-tailed ANSWER: a 3. The probability of committing a Type I error when the null hypothesis is true as an equality is a. the confidence level.

b. β. c. greater than 1. d. the level of significance. ANSWER: d 4. For a given sample size in hypothesis testing, a. the smaller the Type I error, the smaller the Type II error will be. b. the smaller the Type I error, the larger the Type II error will be. c. Type II error will not be affected ...