OPRE Midterm Exam 2 Practice Answers and Insights

OPRE Mid Term Exam 2 Practice Answers  Question 1 2 out of 2 points Which of the following is not a characteristic of a binomial experiment? Selected Answer: Each trial results in two or more outcomes. Answers: There is a sequence of identical trials. Each trial results in two or more outcomes. The trials are independent of each other. The probability of success p is the same from one trial to another.  Question 2 2 out of 2 points The expected number of heads in 100 tosses of an unbiased coin is Selected Answer: 50 Answers: 25 50 75 100  Question 3 2 out of 2 points The variance of a binomial distribution for which n = 100 and p = 0.20 is: Selected Answer: 16 Answers: 100 80 20 16  Question 4 2 out of 2 points The expected number of heads in 250 tosses of an unbiased coin is 125. Selected Answer: True Answers: True False  Question 5 2 out of 2 points If X is a binomial random variable with n = 25, and p = 0.25, then P ( X = 25) = 1.0. Selected Answer: False Answers: True False

 Question 6 2 out of 2 points The number of customers arriving at a department store in a 5-minute period has a binomial distribution. Selected Answer: False Answers: True False  Question 7 2 out of 2 points Which of the following is always true for all probability density functions of continuous random variables? Selected Answer: All of these choices are true. Answers: The probability at any single point is zero. They contain an uncountable number of possible values. The total area under the density function f(x) equals 1. All of these choices are true.  Question 8 2 out of 2 points If the random variable X has a uniform distribution between 40 and 50, then P (35 ≤ X ≤ 45) is: Selected Answer: 0.5 Answers: 1.0 0.5 0.1 undefined.  Question 9 2 out of 2 points Suppose f(x) = 1/4 over the range a ≤ x ≤ b (and 0 elsewhere) , and suppose P ( X > 4) = 1/2. What are the values for a and b ? Selected Answer: 2 and 6 Answers: 0 and 4 2 and 6 Can be any range of x values whose length ( b − a ) equals 4. Cannot answer with the information given.  Question 10 2 out of 2 points In practice, we frequently use a continuous distribution to approximate a discrete one when the number of values the variable can assume is countable but very large. Selected Answer: True Answers: True False

 Question 11 2 out of 2 points If X is a continuous random variable on the interval [0, 10], then P ( X = 5) = f (5) = 1/10. Selected Answer: False Answers: True False  Question 12 2 out of 2 points A standard normal distribution is a normal distribution with: Selected Answer: a mean of zero and a standard deviation of one. Answers: a mean of zero and a standard deviation of one. a mean of one and a standard deviation of zero. a mean always larger than the standard deviation. None of these choices.  Question 13 2 out of 2 points What proportion of the data from a normal distribution is within two standard deviations from the mean? Selected Answer: 0.9544 Answers: 0.3413 0.4772 0.6826 0.9544  Question 14 2 out of 2 points If X has a normal distribution with mean 60 and standard deviation 6, which value of X corresponds with the value z = 1.96? Selected Answer: x = 71.76 Answers: x = 71.76 x = 67.96 x = 61.96 x = 48.24  Question 15 2 out of 2 points Which of the following is not a characteristic for a normal distribution? Selected Answer: The mean is always zero. Answers: It is symmetrical. The mean is always zero.

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The mean, median, and mode are all equal. It is a bell-shaped distribution.  Question 16 2 out of 2 points A larger standard deviation of a normal distribution indicates that the distribution becomes: Selected Answer: flatter and wider. Answers: narrower and more peaked. flatter and wider. more skewed to the right. more skewed to the left.  Question 17 2 out of 2 points Bob took a math test whose mean was 70 and standard deviation was 5. The total points possible was 100. Bob's results were reported to be at the 95th percentile. What was Bob's actual exam score, rounded to the nearest whole number? Selected Answer: 78 Answers: 95 78 75 62  Question 18 2 out of 2 points Bob took a biology exam whose mean was 70 with standard deviation 5. He also took a chemistry exam whose mean was 80 with standard deviation 10. He scored 85 on both exams. On which exam did he do better compared to the other students who took the exam? Selected Answer: He did better on the biology exam, comparatively speaking. Answers: He did better on the biology exam, comparatively speaking. He did better on the chemistry exam, comparatively speaking. He did the same on both exams, relatively speaking. Cannot tell without more information.  Question 19 2 out of 2 points Suppose Bob's exam score was at the 80 th percentile on an exam whose mean was 90. What was Bob's exam score? Selected Answer: Cannot tell without more information. Answers: 76.81 72.00 80.00 Cannot tell without more information.

 Question 20 2 out of 2 points A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50. Selected Answer: True Answers: True False  Question 21 2 out of 2 points A random variable X has a normal distribution with mean 132 and variance 36. If x = 120, its corresponding value of Z is 2.0. Selected Answer: False Answers: True False  Question 22 2 out of 2 points If the value of Z is z = 99, that means you are at the 99 th percentile on the Z distribution. Selected Answer: False Answers: True False  Question 23 2 out of 2 points The probability that Z is less than −2 is the same as one minus the probability that Z is greater than +2. Selected Answer: False Answers: True False  Question 24 2 out of 2 points The standard deviation of the sampling distribution of is also called the: Selected Answer: standard error of the sample mean. Answers: central limit theorem. standard error of the sample mean. finite population correction factor. population standard deviation.  Question 25 2 out of 2 points Random samples of size 49 are taken from an infinite population whose mean is 300 and standard deviation is 21. The mean and standard error of the sample mean, respectively, are: Selected Answer: 300 and 3 Answers: 300 and 21

300 and 3 300 and 0.43 None of these choices.  Question 26 2 out of 2 points Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, is less than 78 is: Selected Answer: 0.9332 Answers: 0.9332 0.5987 1.5000 None of these choices.  Question 27 2 out of 2 points If all possible samples of size n are drawn from an infinite population with a mean of 15 and a standard deviation of 5, then the standard error of the sample mean equals 1.0 for samples of size: Selected Answer: 25 Answers: 5 15 25 None of these choices.  Question 28 2 out of 2 points A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12, respectively. The probability that the sample mean is larger than 70 equals Selected Answer: P ( Z > 1.05) Answers: P ( Z > 70) P ( Z > 2) P ( Z > 0.17) P ( Z > 1.05)  Question 29 2 out of 2 points The expected value of the sampling distribution of the sample mean equals the population mean μ : Selected Answer: for all populations. Answers: only when the population is normally distributed. only when the sample size is large. only when the population is infinite.

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for all populations.  Question 30 2 out of 2 points If a random sample of size n is drawn from a normal population, then the sampling distribution of the sample mean will be: Selected Answer: normal for all values of n . Answers: normal for all values of n . normal only for n > 30. approximately normal for all values of n . approximately normal only for n > 30.  Question 31 2 out of 2 points If all possible samples of size n are drawn from a population, the probability distribution of the sample mean is called the: Selected Answer: sampling distribution of . Answers: standard error of . expected value of . sampling distribution of . normal distribution.  Question 32 2 out of 2 points Suppose X has a distribution that is not normal. The Central Limit Theorem is important in this case because: Selected Answer: it says the sampling distribution of is approximately normal if n is large enough. Answers: it says the sampling distribution of is approximately normal for any sample size. it says the sampling distribution of is approximately normal if n is large enough. it says the sampling distribution of is exactly normal, for any sample size. None of these choices.  Question 33 2 out of 2 points

Which of the following statements about the sampling distribution of is NOT true? Selected Answer: Its standard deviation is equal to the population standard deviation σ . Answers: It is generated by taking all possible samples of size n and computing their sample means. Its mean is equal to the population mean μ . Its standard deviation is equal to the population standard deviation σ . All of these choices are true.  Question 34 2 out of 2 points The standard error of the mean: Selected Answer: All of these choices are true. Answers: is never larger than the standard deviation of the population. decreases as the sample size increases. measures the variability of the mean from sample to sample. All of these choices are true.  Question 35 2 out of 2 points Suppose that 100 items are 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 non-normal probability distribution with μ = 8 ounces and σ = 3 ounces. Which of the following is true about the sampling of ? Selected Answer: All of these choices are true. Answers: Its mean is 8 ounces. Its standard error is 0.3 ounces. Its shape is approximately normal. All of these choices are true.  Question 36 2 out of 2 points Which of the following is true regarding the sampling distribution of the mean for a large sample size? Assume the population distribution is not normal. Selected Answer: It has the same mean as the population, but a different shape and standard deviation. Answers: It has the same shape, mean and standard deviation as the population. It has the same shape and mean as the population, but a different standard deviation. It the same mean and standard deviation as the population, but a different shape. It has the same mean as the population, but a different shape and standard deviation.  Question 37 2 out of 2 points For a sample size of 1, the sampling distribution of the mean is normally distributed:

Selected Answer: only if the population is normally distributed. Answers: regardless of the shape of the population. only if the population values are larger than 30. only if the population is normally distributed. None of these choices.  Question 38 2 out of 2 points The amount of time it takes to complete a final examination is negatively skewed distribution with a mean of 70 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 73.5 minutes is approximately 0. Selected Answer: True Answers: True False  Question 39 2 out of 2 points As the size of the sample is increased, the standard error of decreases. Selected Answer: True Answers: True False  Question 40 2 out of 2 points As the size of the sample is increased, the mean of increases. Selected Answer: False Answers: True False  Question 41 2 out of 2 points As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if: Selected Answer: np and n (1 − p ) are both greater than or equal to 5. Answers: the sample size n is greater than 30. the population proportion p is close to 0.50. the underlying population is normal. np and n (1 − p ) are both greater than or equal to 5.  Question 42 2 out of 2 points Which of the following is always true for all probability density functions of continuous random variables?

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Selected Answer: d. All of these choices are true. Answers: a. The probability at any single point is zero. b. They contain an uncountable number of possible values. c. The total area under the density function f ( x ) equals 1. d. All of these choices are true.  Question 43 2 out of 2 points Which of the following represents a difference between continuous and discrete random variables? Selected Answer: d. All of these choices are true. Answers: a. Continuous random variables assume an uncountable number of values, and discrete random variables do not. b. The probability for any individual value of a continuous random variable is zero, but for discrete random variables it is not. c. Probability for continuous random variables means finding the area under a curve, while for discrete random variables it means summing individual probabilities. d. All of these choices are true.  Question 44 2 out of 2 points Which of the following does not represent a continuous uniform random variable? Selected Answer: c. f ( x ) = 1/3 for x = 4, 5, 6. Answers: a. f ( x ) = 1/2 for x between − 1 and 1, inclusive. b. f ( x ) = 10 for x between 0 and 1/10, inclusive. c. f ( x ) = 1/3 for x = 4, 5, 6. d. None of these choices represents a continuous uniform random variable.  Question 45 2 out of 2 points An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals: Selected Answer: b. 15/ √ 100

Answers: a. 15 b. 15/ √ 100 c. 15/100 d. None of these choices.  Question 46 2 out of 2 points Suppose X has a distribution that is not normal. The Central Limit Theorem is important in this case because: Selected Answer: b. it says the sampling distribution of is approximately normal if n is large enough. Answers: a. it says the sampling distribution of is approximately normal for any sample size. b. it says the sampling distribution of is approximately normal if n is large enough. c. it says the sampling distribution of is exactly normal, for any sample size. d. None of these choices.  Question 47 2 out of 2 points A sample of size n is selected at random from an infinite population. As n increases, the standard error of the sample mean increases. Selected Answer: False Answers: True False  Question 48 2 out of 2 points The sum of all values of f ( x ) over the range of [ a , b ] must equal one. Selected Answer: False Answers: True False  Question 49 2 out of 2 points To be a legitimate probability density function, all possible values of f ( x ) must lie between 0 and 1 (inclusive).

Selected Answer: False Answers: True False  Question 50 2 out of 2 points If X is a continuous random variable on the interval [0, 10], then P ( X = 5) = f (5) = 1/10. Selected Answer: False Answers: True False  Question 51 2 out of 2 points If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference is equal to: Selected Answer: −7 Answers: −7 7 (78 − 85) / (30 − 36) = 1.17 78/30 − 85/36 = 0.24  Question 52 2 out of 2 points Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if Selected Answer: np ≥ 5 and n (1 − p ) ≥ 5 Answers: np ≥ 5 and n (1 − p ) ≥ 5 np ≥ 5 and np (1 − p ) ≥ 5 np ≤ 5 and n (1 − p ) ≤ 5 None of these choices.  Question 53 2 out of 2 points A sample of size 200 is taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion is less than 0.58 is Selected Answer: 0.281 Answers: 0.281 0.719 0.580 0.762

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 Question 54 2 out of 2 points The standard error of the sample proportion gets larger as: Selected Answer: p approaches 0.50 Answers: p approaches 0 p approaches 0.50 p approaches 1.00 None of these choices.  Question 55 2 out of 2 points Recall the rule of thumb used to indicate when the normal distribution is a good approximation of the sampling distribution for the sample proportion . For the combination n = 50, p = 0.05, the rule is satisfied. Selected Answer: False Answers: True False  Question 56 2 out of 2 points If a simple random sample of 300 observations is taken from a population whose proportion p = 0.6, then the expected value of the sample proportion is 0.60. Selected Answer: True Answers: True False  Question 57 2 out of 2 points Which of the following is a characteristic for a good estimator? Selected Answer: All of these choices are true. Answers: Being unbiased Being consistent Having relative efficiency All of these choices are true.  Question 58 2 out of 2 points A point estimator is defined as: Selected Answer: a single value that estimates an unknown population parameter. Answers: a range of values that estimates an unknown population parameter. a range of values that estimates an unknown sample statistic.

a single value that estimates an unknown population parameter. a single value that estimates an unknown sample statistic.  Question 59 2 out of 2 points An unbiased estimator of a population parameter is defined as: Selected Answer: an estimator whose expected value is equal to the parameter. Answers: an estimator whose expected value is equal to the parameter. an estimator whose variance is equal to one. an estimator whose expected value is equal to zero. an estimator whose variance goes to zero as the sample size goes to infinity.  Question 60 2 out of 2 points An estimator is said to be consistent if: Selected Answer: the difference between the estimator and the population parameter grows smaller as the sample size grows larger. Answers: it is an unbiased estimator. the variance of the estimator is zero. the difference between the estimator and the population parameter stays the same as the sample size grows larger. the difference between the estimator and the population parameter grows smaller as the sample size grows larger.  Question 61 2 out of 2 points If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be: Selected Answer: relatively efficient. Answers: a biased estimator. relatively efficient. consistent. relatively unbiased.  Question 62 2 out of 2 points The problem with relying on a point estimate of a population parameter is that: Selected Answer: All of these choices are true. Answers: it is virtually certain to be wrong. it doesn't have the capacity to reflect the effects of larger sample sizes. it doesn't tell us how close or far the point estimate might be from the parameter. All of these choices are true.  Question 63

2 out of 2 points The sample variance s 2 is an unbiased estimator of the population variance σ 2 when the denominator of s 2 is Selected Answer: n − 1 Answers: n + 1 n n − 1  Question 64 2 out of 2 points The 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 took a sample and found the mean to be 880 books. She provides the librarian with an interval estimate of between 790 and 970 books checked out per day. An efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress is: Selected Answer: 880 Answers: 790 880 90 None of these choices.  Question 65 2 out of 2 points The sample proportion is a consistent estimator of the population proportion p because it is unbiased and the variance of is p (1 − p ) / n , which grows smaller as n grows larger. Selected Answer: True Answers: True False  Question 66 2 out of 2 points A specific confidence interval obtained from data will always correctly estimate the population parameter. Selected Answer: False Answers: True False  Question 67 2 out of 2 points The term 1 − α refers to: Selected Answer: the confidence level. Answers: the probability that a confidence interval does not contain the population parameter. the confidence level.

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the level of unbiasedness. the level of consistency.  Question 68 2 out of 2 points The value for a 95% confidence interval estimate for a population mean μ is Selected Answer: 1.96 Answers: 0.95 0.025 1.65 1.96  Question 69 2 out of 2 points In developing an interval estimate for a population mean, the population standard deviation σ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had σ equaled 20, the interval estimate would be Selected Answer: 50.92 ± 4.28 Answers: 60.92 ± 2.14 50.92 ± 12.14 101.84 ± 4.28 50.92 ± 4.28  Question 70 2 out of 2 points In developing an interval estimate for a population mean, a sample of 50 observations was used. The interval estimate was 19.76 ± 1.32. Had the sample size been 200 instead of 50, the interval estimate would have been: Selected Answer: 19.76 ± .66 Answers: 19.76 ± .33 19.76 ± .66 19.76 ± 5.28 None of these choices.  Question 71 2 out of 2 points After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. In order to correct this problem, you need to: Selected Answer: increase the sample size. Answers: increase the population standard deviation. increase the sample size. increase the level of confidence. increase the sample mean.

 Question 72 2 out of 2 points Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: Selected Answer: 66.15 Answers: 56.34 62.96 6.62 66.15  Question 73 2 out of 2 points Which of the following conditions does not allow you to use the formula to estimate μ ? Selected Answer: Population has any distribution and n is any size. Answers: Population is normally distributed and the population variance is known. Population is not normally distributed but n is large; population variance is known. Population has any distribution and n is any size. All of these choices allow you to use the formula.  Question 74 2 out of 2 points Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean? Selected Answer: The value of the population mean. Answers: A point estimate of the population mean. The standard error of the sampling distribution of the sample mean. The confidence level. The value of the population mean.  Question 75 2 out of 2 points A 99% confidence interval estimate of the population mean μ can be interpreted to mean: Selected Answer: All of these choices are true. Answers: if all possible sample are taken and confidence intervals created, 99% of them would include the true population mean somewhere within their interval. we have 99% confidence that we have selected a sample whose interval does include the population mean. we estimate that the population mean falls between the lower and upper confidence limits, and this type of estimator is correct 99% of the time. All of these choices are true.  Question 76 2 out of 2 points

One can reduce the width of a confidence interval by taking a smaller sample size. Selected Answer: False Answers: True False  Question 77 2 out of 2 points The width of a 95% confidence interval is 0.95. Selected Answer: False Answers: True False  Question 78 2 out of 2 points Given a mean of 2.1 and a standard deviation of 0.7, a 90% confidence interval will be 2.1 ± 0.7. Selected Answer: False Answers: True False  Question 79 2 out of 2 points Other things being equal, as the confidence level increases, the width of the confidence interval increases. Selected Answer: True Answers: True False  Question 80 2 out of 2 points To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least: Selected Answer: 166 Answers: 166 167 13 None of these choices.  Question 81 2 out of 2 points The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was: Selected Answer: 90% Answers: 99% 95%

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90% None of these choices.  Question 82 2 out of 2 points The probability of a Type I error is denoted by: (this questions pertains to the last section of Lecture 9, which is a self-study, non-exam content) Selected Answer: α Answers: β 1 − β α 1 − α  Question 83 2 out of 2 points The hypothesis of most interest to the researcher is: Selected Answer: the alternative hypothesis. Answers: the alternative hypothesis. the null hypothesis. both hypotheses are of equal interest. Neither hypothesis is of interest.  Question 84 2 out of 2 points A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is: Selected Answer: H 0 : μ = 1200 vs. H 1 : μ > 1200 Answers: H 0 : μ = 1200 vs. H 1 : μ < 1200 H 0 : μ > 1200 vs. H 1 : μ = 1200 H 0 : μ = 1200 vs. H 1 : μ > 1200 H 0 : μ < 1200 vs. H 1 : μ = 1200  Question 85 2 out of 2 points Which of the following conclusions is not an appropriate conclusion from a hypothesis test? Selected Answer: Accept H 0 . Sufficient evidence to support H 0 . Answers: Reject H 0 . Sufficient evidence to support H 1 . Fail to reject H 0 . Insufficient evidence to support H 1 . Accept H 0 . Sufficient evidence to support H 0 . All of these choices are true.  Question 86 2 out of 2 points

A null hypothesis is a statement about the value of a population parameter. Selected Answer: True Answers: True False  Question 87 2 out of 2 points Increasing the probability of a Type I error will increase the probability of a Type II error. (this questions pertains to the last section of Lecture 9, which is a self-study, non-exam content) Selected Answer: False Answers: True False  Question 88 2 out of 2 points In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data. Selected Answer: True Answers: True False  Question 89 2 out of 2 points The statement of the null hypothesis always includes an equals sign (=). Selected Answer: True Answers: True False  Question 90 2 out of 2 points In testing the hypotheses H 0 : μ = 50 vs. H 1 : μ ≠ 50, the following information is known: n = 64, = 53.5, and σ = 10. The standardized test statistic z equals: Selected Answer: 2.80 Answers: 1.96 −2.80 2.80 −1.96  Question 91 2 out of 2 points In testing the hypotheses H 0 : μ = 75 vs. H 1 : μ < 75, if the value of the test statistic z equals −2.42, then the p -value is: Selected Answer: 0.0078 Answers: 0.5078

2.4200 0.9922 0.0078  Question 92 2 out of 2 points In testing the hypotheses H 0 : μ = 800 vs. H 1 : μ ≠ 800, if the value of the test statistic equals 1.75, then the p -value is: Selected Answer: 0.0802 Answers: 0.0401 0.0802 0.4599 0.9599  Question 93 2 out of 2 points In testing the hypothesis H 0 : μ = 100 vs. H 1 : μ > 100, the p -value is found to be 0.074, and the sample mean is 105. Which of the following statements is true? Selected Answer: The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. Answers: The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is 0.074. The probability that the population mean is larger than 100 is 0.074. None of these choices.  Question 94 2 out of 2 points Statisticians can translate p -values into several descriptive terms. Suppose you typically reject H 0 at level 0.05. Which of the following statements is correct? Selected Answer: All of these choices are true. Answers: If the p -value < 0.001, there is overwhelming evidence to infer that the alternative hypothesis is true. If 0.01 < p -value < 0.05, there is evidence to infer that the alternative hypothesis is true. If p -value > 0.10, there is no evidence to infer that the alternative hypothesis is true. All of these choices are true.  Question 95 2 out of 2 points If we do not reject the null hypothesis, we conclude that: Selected Answer: there is not enough statistical evidence to infer that the alternative hypothesis is true. Answers: there is enough statistical evidence to infer that the alternative hypothesis is true.

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there is not enough statistical evidence to infer that the alternative hypothesis is true. there is enough statistical evidence to infer that the null hypothesis is true. there is not enough statistical evidence to infer that the null hypothesis is true.  Question 96 2 out of 2 points The p -value of a test is the: Selected Answer: smallest α at which the null hypothesis can be rejected. Answers: smallest α at which the null hypothesis can be rejected. largest α at which the null hypothesis can be rejected. smallest α at which the null hypothesis cannot be rejected. largest α at which the null hypothesis cannot be rejected.  Question 97 2 out of 2 points We have created a 95% confidence interval for μ with the results (10, 25). What conclusion will we make if we test H 0 : μ = 26 vs. H 1 : μ ≠ 26 at α = 0.025? Selected Answer: We cannot tell from the information given. Answers: Reject H 0 in favor of H 1 Accept H 0 in favor of H 1 Fail to reject H 0 in favor of H 1 We cannot tell from the information given.  Question 98 2 out of 2 points The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years. What is the p -value associated with the test statistic? Selected Answer: 0.0418 Answers: 0.9582 1.7300 0.0418 0.0836  Question 99 2 out of 2 points The p -value is the probability that the null hypothesis is true. Selected Answer: False Answers: True False

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 Question 100 2 out of 2 points A p -value is a probability, and must be between 0 and 1. Selected Answer: True Answers: True False  Question 101 10 out of 10 points A random variable X has a normal distribution with mean 132 and variance 36. If x = 120, its corresponding value of Z is 2.0. Selected Answer: False Answers: True False  Question 102 10 out of 10 points The probability that standard normal random variable Z is less than − 2 is the same as one minus the probability that Z is greater than +2. Selected Answer: False Answers: True False  Question 103 10 out of 10 points Tanner took a statistics test whose mean was 80 and standard deviation was 5. The total points possible was 100. Tanner's score was 2 standard deviations below the mean. What was Tanner's score, rounded to the nearest whole number? Selected Answer: B. 70 Answers: A. 78 B. 70 C. 90 D. None of the above  Question 104 10 out of 10 points A larger standard deviation of a normal distribution indicates that the distribution becomes: Selected Answer: B. flatter and wider. Answers: A. narrower and more peaked. B. flatter and wider. C.

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more skewed to the right. D. more skewed to the left.  Question 105 0 out of 10 points The sampling distribution of sample proportion is approximately normal if the sample size is more than 30. Selected Answer: True Answers: True False  Question 106 10 out of 10 points The statement of the null hypothesis always includes an equals sign (=). Selected Answer: True Answers: True False  Question 107 10 out of 10 points Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 5% level of significance were used in testing the hypotheses H 0 : μ = 201 vs. H 1 : μ< 201, the null hypothesis: Selected Answer: A. would be rejected. Answers: A. would be rejected. B. would be accepted. C. would fail to be rejected. D. Not enough information to make a decision.  Question 108 0 out of 10 points The width of a confidence interval estimate for a population proportion will be: Selected Answer: C. narrower for 99% confidence than for 95% confidence. Answers: A. narrower when the sample proportion is 0.50 than when the sample proportion is 0.20. B. wider for a sample size of 100 than for a sample size of 50. C. narrower for 99% confidence than for 95% confidence. D. narrower for 90% confidence than for 95% confidence.

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OPRE 6301 Practice Test 2 Answers

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