Statistics Final
100
A
13. For the dataset "volumes of milk dispensed into 2-gallon milk cartons," should you use the mean or the median to describe the center? a) Mean b) Median c) Neither
A
16
A
18
A
2. Airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. What is the variable of interest? a) Number of bags weighing more than 75 pounds. b) Average weight of the bags. c) Each piece of baggage. d) The airport administrators.
A
24. Attendance at a university's basketball games follows a normal distribution with mean μ = 8,000 and standard deviation σ = 1,000. Estimate the percentage of games that have between 7,000 to 9,000 people in attendance. a) 68% b) 95% c) 99.7% d) 100%
A
25. Which one of the following is a FALSE statement about the standard normal curve? a) Its standard deviation σ can vary with different datasets. b) It is bell-shaped. c) It is symmetric around 0. d) Its mean μ = 0.
A
29. Which one of the following is a FALSE statement about the standard normal distribution? a) The mean is greater than the median. b) It is symmetric. c) It is bell-shaped. d) It has one peak.
A
31. A correct interpretation of the statement "The probability that a child delivered in a certain hospital is a girl is 0.50" would be which one of the following? a) Over a long period of time, there will be equal proportions of boys and girls born at that hospital. b) In the next two births at that hospital, there will be exactly one boy and one girl. c) To make sure that a couple has two girls and two boys at that hospital, they only need to have four children. d) A computer simulation of 100 births for that hospital would produce exactly 50 girls and 50 boys.
A
39. Would the following random variable, X, be discrete or continuous? X = the time required to run a marathon. a) Continuous b) Discrete c) Neither d) Both
A
4. What type of data is produced by the answer choices for this question? * How many times have you accessed the internet this week? - None - Once or twice - Three or four times - More than four times a) categorical b) quantitative c) neither d) both
A
44. Which of the following sampling schemes describes a simple random sample of 200 undergraduate students at a large university? a) Obtain a list of the undergraduate students at the large university; assign consecutive numbers to the students on the list; use a random number table to select 200 university students. b) Obtain a list of all freshmen, sophomores, juniors, and seniors; use a random number table to randomly select 50 students from each class. c) Randomly select 10 colleges; within each college, randomly select 5 majors; from each of the selected majors randomly select 4 undergraduate students.
A
46. Using a local telephone book to select a simple random sample could introduce what type of bias? a) Undercoverage bias b) Nonresponse bias c) Response bias d) Question wording bias
A
49. True or false: Bias can occur in surveys where the participants are selected using a simple random sample. a) True b) False
A
5. For the Internet access data in the previous question, what is the BEST method of displaying the data? a) bar graph b) boxplot c) histogram d) scatterplot
A
52. We wish to estimate the mean price, μ, of all hotel rooms in Las Vegas. The Convention Bureau of Las Vegas did this in 1999 and used a sample of n = 112 rooms. In order to get a better estimate of μ than the 1999 survey, we should a) Take a larger sample because the sample mean will be closer to μ. b) Take a smaller sample since we will be less likely to get outliers. c) Take a different sample of the same size since it does not matter what n is.
A
55. The theoretical sampling distribution of X ̅ a) Gives the values of X ̅ from all possible samples of size n from the same population. b) Provides information about the shape, center, and spread of the values in a single sample. c) Can only be constructed from the results of a single random sample of size n. d) Is another name for the histogram of values in a random sample of size n.
A
59. Which of the following would result in a decrease in the spread of the approximate sampling distribution of X ̅? a) Increasing the sample size. b) Increasing the number of samples taken. c) Increasing the population standard deviation d) Decreasing the value of the population mean.
A
61. What is statistical inference on μ? a) Drawing conclusions about a population mean based on information contained in a sample. b) Drawing conclusions about a sample mean based on information contained in a population. c) Drawing conclusions about a sample mean based on the measurements in that sample. d) Selecting a set of data from a large population.
A
72. Why do we need a normal population or large sample size to do inference on μ? a) So that the sampling distribution of X ̅ is normal or approximately normal. b) So that the distribution of the sample data is normal or approximately normal. c) So that X ̅ equals μ. d) So that σ is known.
A
77. A group of researchers wanted to know if there was a difference in average yearly income taxes paid between residents of two very large cities in the midwestern United States. The average for the first city was $6,505 and for the second city, it was $6,511. The difference provided a P-value of 0.0007. Were these results practically significant? a) No, because a $6 difference is probably too small to really matter. b) No, because the P-value is small. c) Yes, because the P-value is small. d) Yes, because the difference of $6 is bigger than 0.
A
79. Increasing the confidence level will a) Increase the margin of error. b) Decrease the margin of error. c) Neither
A
82. A survey-taker asks whether each person in a random sample of 20 college students is over the age of 21. X is the number of people who are over 21. According to university records, 35% of all college students are over 21 years old. Does X have a binomial distribution? a) Yes. b) No, because there is not a fixed number of observations. c) No, because the observations are not all independent. d) No, because there are more than two possible outcomes for each observation. e) No, because the probability of success for each observation is not the same.
A
90. When does the normal approximation to the binomial give the most accurate answer? a) When n is big. b) When n is small. c) When p is big. d) When p is small.
A
92. The theoretical sampling distribution of p ̂ a) Gives the values of p ̂ from all possible samples of size n from the same population. b) Provides information about the shape, center, and spread of the values in a single sample. c) Can only be constructed from the results of a single random sample of size n. d) Is another name for the histogram of the values in a random sample of size n.
A
98. The margin of error covers a) Random sampling error. b) Undercoverage error. c) Non-response error. d) All of the above.
A
14
B
15. The shape of the boxplot above can be described as: a) Bi-modal b) Left-skewed c) Right-skewed d) Symmetric e) Uniform
B
17
B
20
B
23
B
28
B
3. Would the variable "monthly rainfall in Michigan" be considered a categorical or quantitative variable? a) categorical b) quantitative c) neither d) both
B
30
B
32. From a computer simulation of rolling a fair die ten times, the following data were collected on the showing face: 5 5 1 3 2 1 5 6 5 1 What is a correct conclusion to make about the next ten rolls of the same die? a) The probability of rolling a 5 is greater than the probability of rolling anything else. b) Each face has exactly the same probability of being rolled. c) We will see exactly three faces showing a 1 since it is what we saw in the first experiment. d) The probability of rolling a 4 is 0, and therefore we will not roll it in the next ten rolls.
B
33. Which of the following events would NOT be considered a random phenomenon? a) The event that the next passing car will be blue. b) The event that a student gets an answer correct after hours of studying. c) The event that a person's height is bigger than their armspan. d) The event that the next customer at a grocery store buys bananas.
B
36. What is the probability that the couple has either one or two girls? a) 0.375 b) 0.375 + 0.375 = 0.750 c) 1 - 0.125 = 0.825 d) 0.500
B
38. Would the following random variable, X, be discrete or continuous? X = the number of sales at the drive-through during the lunch rush at the local fast food restaurant. a) Continuous b) Discrete c) Neither d) Both
B
40. Would the following random variable, X, be discrete or continuous? X = the number of fans in a football stadium. a) Continuous b) Discrete c) Neither d) Both
B
41. In 1993, presidential candidate Ross Perot appeared on television to voice his opinions on government reform. To gauge public opinion, Perot urged viewers to fill out the survey appearing in that week's issue of TV Guide. Of the approximately 1.4 million respondents, 98% agreed with Ross Perot's platform on health care reform. What type of sampling method was used? a) Convenience sample b) Voluntary response sample c) Simple random sample d) Random-digit dialing
B
42. A researcher is conducting a survey at the mall. She decides to assign numbers to the people entering the mall using the order in which they enter. She then uses a random number table to choose the first person to question and then decides to choose every 20th person after that. Is this a simple random sample? a) True b) False
B
50. Suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. You take an SRS of 200 of the 25,000 undergraduate students and an SRS of 100 of 5,000 graduate students. Is this a simple random sample? a) True b) False
B
51. The average fuel tank capacity of all cars made by Ford is 14.7 gallons. This value represents a a) Parameter because it is an average from all possible cars. b) Parameter because it is an average from all Ford cars. c) Statistic because it is an average from a sample of all cars. d) Statistic because it is an average from a sample of American cars.
B
56. What does σ/√n measure? a) The spread of the population. b) The spread of the X ̅'s. c) Different values X ̅ could be. d) None of the above
B
60. Time spent working out at a local gym is normally distributed with mean μ = 43 minutes and standard deviation σ = 6 minutes. The gym took a sample of size n = 24 from its patrons. What is the distribution of X ̅? a) Normal with mean μ = 43 minutes and standard deviation σ = 6 minutes. b) Normal with mean μ = 43 minutes and standard deviation σ = 6/√24 minutes. c) Cannot be determined because the sample size is too small.
B
64. What do we hope to capture within a confidence interval? a) The unknown confidence level. b) The unknown parameter. c) The unknown statistic. d) The parameter estimate. e) The margin of error. f) The sample size.
B
66. We reject the null hypothesis whenever a) P-value > α. b) P-value ≤ α. c) P-value ≠ α. d) P-value ≠ μ.
B
68. Which of the following is a conservative choice for significance level? a) 0 b) 0.01 c) 0.25 d) 0.50 e) 0.75 f) 1
B
75. A certain manufacturer of paints uses an additive to get the drying time for a specific paint to be 75 minutes. If there's too much additive, the drying time could be longer than specified but too little additive will decrease the drying time. In testing the amount of additive, they use these hypotheses: H0: μ = 7 ml vs. Ha: μ ≠ 7 ml. Which of the following would be an implication of having a small α? a) Concluding that the mean amount of additive is different from 7 ml more often. b) Concluding that the mean amount of additive is not different from 7 ml more often. c) Neither
B
80. Increasing the sample size will a) Increase the margin of error. b) Decrease the margin of error. c) Neither
B
84. A fair die is rolled and the number of dots on the top face is noted. X is the number of times we have to roll in order to have the face of the die show a 2. Does X have a binomial distribution? a) Yes. b) No, because there is not a fixed number of observations. c) No, because the observations are not all independent. d) No, because there are more than two possible outcomes for each observation. e) No, because the probability of success for each observation is not the same.
B
86. A fair die is rolled 8 times and X is the number of times the face of the die shows an even number. What is the probability that X > 1? a) 0.0039 b) 0.9961 c) 0.2326 d) 0.7674
B
9
B
91. Which of the following symbols represents the sample proportion? a) p b) p ̂ c) σ_p ̂ d) P-value
B
95. Ten percent of all customers of Cheap Foods regularly purchase Good-Enuf Brand Chicken Fingers. We plan to ask a random sample of 45 Cheap Foods customers if they regularly purchase Good-Enuf Chicken Fingers. We will then calculate from the responses. Is the shape of the sampling distribution of close enough to normal to use the normal distribution to compute probabilities on ? a) Yes, because n > 30. b) No, because np = (45) (0.10) = 4.5 which is < 10. c) No, because we only have data from one sample. d) We cannot know the shape without knowing how many of the 45 customers purchase Good-Enuf Chicken Fingers.
B
1. Airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. What is the individual? a) Number of bags weighing more than 75 pounds. b) Average weight of the bags. c) Each piece of baggage. d) The airport administrators.
C
11. Find the median of the following 9 numbers: 43 54 55 63 67 68 69 77 85 a) 65 b) 64 c) 67 d) 64.6
C
12. For the data in the previous question, 43 54 55 63 67 68 69 77 85 Suppose that the last data point is actually 115 instead of 85. What effect would this new maximum have on our value for the median of the dataset? a) Increase the value of the median. b) Decrease the value of the median. c) Not change the value of the median. d) Eliminate the median.
C
19. Which of the following statements is TRUE? a) Standard deviation has no unit of measurement. b) Standard deviation is either positive or negative. c) Standard deviation is inflated by outliers. d) Standard deviation is used even when the mean is not an appropriate measure of center.
C
22. Which one of the following is a FALSE statement about density curves? a) Always on or above the x-axis. b) Area under the curve within an interval is the proportion of values expected in that interval. c) Total area under the curve depends on the shape of the curve. d) The median divides the area under the curve in half. e) The mean is the balancing point of the density curve.
C
26. Which one of the following is a FALSE statement about a standardized value (z-score)? a) It represents how many standard deviations an observation lies from the mean. b) It represents in which direction an observation lies from the mean. c) It is measured in the same units as the variable. d) Its formula is (x-μ)/σ
C
47. Which of the following would not be in the SRS of 4 units taken from a group of 60 where the units are labeled 01 to 60. Use the line from the table of random digits shown below 96767 35964 23822 96012 94591 65194 50842 53372 a) 29 b) 60 c) 12 d) 59
C
48. If people tend to respond differently to a question depending on whether the interviewer is male or female, which type of bias is present? a) Undercoverage bias b) Nonresponse bias c) Response bias d) Question wording bias
C
53. The Law of Large Numbers says that a) If the population is large, the estimate for μ would be better than if the population was small. b) X ̅ is a good estimate for μ as long as the size of the population was large. c) If we increase our sample size, X ̅ will be a better estimate for μ. d) As long as the values for x are large, our estimate for μ will be good.
C
54. Which of the following is true? a) The shape of the sampling distribution of X ̅ is always bell-shaped. b) The shape of the sampling distribution of X ̅ gets closer to the shape of the population distribution as n gets large. c) The shape of the sampling distribution of X ̅ gets approximately normal as n gets large. d) The mean of the sampling distribution of X ̅ gets closer to µ as n gets large.
C
6. In the dataset represented by the following stemplot, how many times does the number "28" occur? Leaf unit = 1.0. 0 |9 1 |246999 2 |111134567888999 3 |000112222345666699 4 |001445 5 |0014 6 |7 7 |3 a) 0 b) 1 c) 3 d) 4
C
62. The purpose of a confidence interval for μ is a) To give a range of reasonable values for the level of confidence. b) To give a range of reasonable values for the sample mean. c) To give a range of reasonable values for the population mean. d) To give a range of reasonable values for the difference between the sample mean and the population mean.
C
67. The significance level is denoted by a) μ b) σ c) α d) P-value
C
69. Suppose the P-value for a hypothesis test is 0.304. Using α = 0.05, what is the appropriate conclusion? a) Reject the null hypothesis. b) Reject the alternative hypothesis. c) Do not reject the null hypothesis. d) Do not reject the alternative hypothesis.
C
7
C
70. Suppose a significance test is being conducted using a significance level of 0.10. If a student calculates a P-value of 1.9, the student a) Should reject the null hypothesis. b) Should fail to reject the null hypothesis. c) Made a mistake in calculating the P-value.
C
71. The conditions for doing inference on μ using the standard normal distribution do NOT include: a) A simple random sample of size n. b) A normal population or sample size large enough to apply the Central Limit Theorem. c) A known value of μ. d) A known value of σ.
C
73. Which of the following components of the margin of error in a confidence interval for μ does a researcher NOT have the chance to select? a) Confidence level. b) Sample size. c) Population standard deviation.
C
74. What sample size should be used to estimate μ within ±7 with 95% confidence if σ = 23? a) n = (1.645∙23/7)2 = 30 b) n = (1.645∙23/7)2 = 29 c) n = (1.96∙23/7)2 = 42 d) n = (1.96∙23/7)2 = 41
C
76. A group of researchers wanted to know if there was a difference in average yearly income taxes paid between residents of two very large cities in the midwestern United States. The average for the first city was $6,505 and for the second city, it was $6,511. The difference provided a P-value of 0.0007. Were these results statistically significant? a) No, because a $6 difference is probably too small to really matter. b) No, because the P-value is small. c) Yes, because the P-value is small. d) Yes, because the difference of $6 is bigger than 0.
C
8. What shape would you say the data take? a) Bi-modal b) Left-skewed c) Right-skewed d) Symmetric e) Uniform
C
93. Which of the following is true? a) The shape of the sampling distribution of p ̂ is always bell-shaped. b) The shape of the sampling distribution of p ̂ gets closer to the shape of the population distribution as n gets large. c) The shape of the sampling distribution of p ̂ becomes approximately normal as n gets large.
C
94. Which of the following best describes the mean of the sampling distribution of p ̂? a) As n increases, the mean of the sampling distribution of p ̂ gets closer to p. b) As n increases, the mean of the sampling distribution of p ̂ gets closer to x ̅. c) Regardless of the value of n, the mean of the sampling distribution of p ̂ is equal to p.
C
96. The purpose of a confidence interval for p is a) To give a range of reasonable values for the level of confidence. b) To give a range of reasonable values for the sample proportion. c) To give a range of reasonable values for the population proportion. d) To give a range of reasonable values for the difference between the sample proportion and the population proportion.
C
10
D
21. Which of the following quantities would give us information about a sample? a) μ b) p c) σ d) X ̅
D
27. Rachael got a 670 on the analytical portion of the Graduate Record Exam (GRE). If GRE scores are normally distributed and have mean μ = 600 and standard deviation σ = 30, what is her standardized score? a) (600-670)/30 b) (30*670)/600 c) √((670-600)/30) d) (670-600)/30
D
34
D
35. What is the probability that the couple does NOT have girls for all three children? a) 0.125 b) 0.125 c) 0.125 + 0.375 = 0.500 d) 1 - 0.125 = 0.825
D
37
D
43
D
45. A Gallup poll sponsored by the disposable diaper industry asked "It is estimated that disposable diapers account for less than 2% of the trash in today's landfills. In contrast, beverage containers, third-class mail, and yard waste are estimated to account for about 21% of the trash in landfills. Given this, in your opinion, would it be fair to ban disposable diapers?" Which type of bias does this poll suffer from? a) Undercoverage bias b) Nonresponse bias c) Response bias d) Question wording bias
D
57. Which is a true statement about the Central Limit Theorem? a) We need to take repeated samples in order to estimate μ. b) It only applies to populations that are Normally distributed. c) It says that the distribution of X ̅'s will have the same shape as the population. d) It requires the condition that the sample size, n, is large and that the samples were drawn randomly.
D
58. What effect does increasing the sample size, n, have on the center of the sampling distribution of X ̅? a) The mean of the sampling distribution gets closer to the mean of the population. b) The mean of the sampling distribution gets closer to 0. c) The variability of the population mean is decreased. d) It has no effect. The mean of the sampling distribution always equals the mean of the population.
D
65. A consumer advocate is interested in evaluating the claim that a new granola cereal contains "4 ounces of cashews in every bag." The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews. What is the size of the observed effect? a) 3.68 oz. b) -3.68 oz. c) 4 - 3.68 = 0.32 oz. d) 3.68 - 4 = - 0.32 oz.
D
78. A researcher is interested in estimating the mean yield (in bushels per acre) of a variety of corn. From her sample, she calculates the following 95% confidence interval: (118.74, 128.86). Her colleague wants to test (at α = 0.05) whether or not the mean yield for the population is different from 120 bushels per acre. Based on the given confidence interval, what can the colleague conclude? a) The mean yield is different from 120 and it is statistically significant. b) The mean yield is not different from 120 and it is statistically significant. c) The mean yield is different from 120 and it is not statistically significant. d) The mean yield is not different from 120 and it is not statistically significant.
D
81. A survey-taker asks the age of each person in a random sample of 20 people. X is the age for the individuals. Does X have a binomial distribution? a) Yes. b) No, because there is not a fixed number of observations. c) No, because the observations are not all independent. d) No, because there are more than two possible outcomes for each observation.
D
85
D
87
D
88. Suppose that for a randomly selected high school student who has taken a college entrance exam, the probability of scoring above a 650 is 0.30. A random sample of n = 90 high school students was selected. If we want to calculate the probability that at least 20 of these students scored above a 650, what distribution would be the best for us to use? Note that np=27 and √(np(1-p) )=0.435 a) Binomial (n = 90, p = 0.30) b) Binomial (μ = 27, σ = 0.435) c) Normal (n = 90, p = 0.30) d) Normal (μ = 27, σ = 0.435)
D
89. Why would we want to use the normal approximation to the binomial instead of just using the binomial distribution? a) The normal distribution is more accurate. b) The normal distribution uses the mean and the standard deviation. c) The normal distribution works all the time, so use it for everything. d) The binomial distribution is awkward and takes too long if you have to sum up many probabilities. The binomial distribution looks like the normal distribution if n is large. e) The binomial distribution is awkward and takes too long if you have to multiply many probabilities. The binomial distribution looks like the normal distribution if n is large.
D
99. When an opinion poll states with 95% confidence the margin of error for the sample percentage is plus or minus 3 percentage points, this means that a) Between 92% and 98% of the people chosen for the sample were contacted. b) The percentage of people who said "Yes" to the question was between 92% and 98%. c) 95% of the time, the sample percentage differs from the true population value by exactly 3 percentage points. d) 95% of all samples chosen using the same method will give a sample percent within 3 percentage points of the true population value.
D
83. A certain test contains 10 multiple-choice problems. For five of the problems, there are four possible answers, and for the other five there are only three possible answers. X is the number of correct answers a student gets by simply guessing. Does X have a binomial distribution? a) Yes. b) No, because there is not a fixed number of observations. c) No, because the observations are not all independent. d) No, because there are more than two possible outcomes for each observation. e) No, because the probability of success for each observation is not the same.
E
97. The confidence interval formula for p does NOT include a) The sample proportion. b) The z* value for specified level of confidence. c) The margin of error. d) The sample size. e) The population size.
E
63. The confidence interval formula for μ does NOT include a) The sample mean. b) The population standard deviation. c) The z* value for specified level of confidence. d) The margin of error. e) The sample size. f) The population size.
F
