Homework Stats 2
swthny007
sample_questions_for_final.docx1) Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called
A) statistical inference.
B) the scientific method.
C) sampling.
D) descriptive statistics.
Answer: D
2) Which of the following is NOT an element of descriptive statistical problems?
A) an inference made about the population based on the sample
B) the population or sample of interest
C) tables, graphs, or numerical summary tools
D) identification of patterns in the data
Answer: A
3) Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wanted to estimate the textbook costs of first-year students at Drummand. To do so, she monitored the textbook cost of 250 first-year students and found that their average textbook cost was $600 per semester. Identify the population of interest to the researcher.
A) all Drummand University students
B) all college students
C) all first-year Drummand University students
D) the 250 students that were monitored
Answer: C
4) Researchers are concerned that the weight of the average American school child is increasing, implying, among other things, that children's clothing should be manufactured and marketed in larger sizes. If X is the weight of school children sampled in a nationwide study, then X is an example of
A) a categorical random variable.
B) a discrete random variable.
C) a continuous random variable.
D) a parameter.
Answer: C
5) The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. The answer on "whether you visited campus bars on the weekend before the final exam week" from students in the sample is an example of
A) a categorical random variable.
B) a discrete random variable.
C) a continuous random variable.
D) a parameter.
Answer: A
6) The British Airways Internet site provides a questionnaire instrument that can be answered electronically. Which of the four methods of data collection is involved when people complete the questionnaire?
A) published sources
B) experimentation
C) surveying
D) observation
Answer: C
7) A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. Shown below is a pie chart of the results. What percentage of the class took the course prior to reaching their senior year?
A) 14%
B) 44%
C) 54%
D) 86%
Answer: D
8) One of the developing countries is experiencing a baby boom, with the number of births rising for the fifth year in a row, according to a BBC News report. Which of the following is best for displaying this data?
A) a Pareto chart
B) a two-way classification table
C) a histogram
D) a time-series plot
Answer: D
9) In a survey, 150 executives were asked what they think is the most common mistake candidates make during job interviews. Six different mistakes were given. Which of the following is the best for presenting the information?
A) a bar chart
B) a histogram
C) a stem-and-leaf display
D) a contingency table
Answer: A
The ordered array below resulted from selecting a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.
Defects
1 2 4 4 5 5 6 7 9 9 12 12 15
17 20 21 23 23 25 26 27 27 28 29 29
10) Referring to the table above, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the frequency of the "20 but less than 25" class would be ________.
Answer: 4
11) Referring to the table above, if a frequency distribution for the defects data is constructed, using "0 but less than 5" as the first class, the relative frequency of the "15 but less than 20" class would be ________.
12) Which of the following statistics is NOT a measure of central tendency?
A) arithmetic mean
B) median
C) mode
D) Q3
Answer: D
13) Which descriptive summary measures are considered to be resistant statistics?
A) the arithmetic mean and standard deviation
B) the interquartile range and range
C) the mode and variance
D) the median and interquartile range
Answer: D
14) According to the empirical rule, if the data form a "bell-shaped" normal distribution, ________ percent of the observations will be contained within 1 standard deviation around the arithmetic mean.
A) 68.26
B) 75.00
C) 88.89
D) 93.75
Answer: A
15) According to the Chebyshev rule, at least 93.75% of all observations in any data set are contained within a distance of how many standard deviations around the mean?
A) 1
B) 2
C) 3
D) 4
Answer: D
16) True or False: If the data set is approximately bell-shaped, the empirical rule will more accurately reflect the greater concentration of data close to the mean as compared to the Chebyshev rule.
Answer: TRUE
17) If two events are mutually exclusive, what is the probability that one or the other occurs?
A) 0
B) 0.50
C) 1.00
D) cannot be determined from the information given
18) If two equally likely events A and B are mutually exclusive and collectively exhaustive, what is the probability that event A occurs?
A) 0.
B) 0.50
C) 1.00
D) cannot be determined from the information given
Answer: B
19) If two equally likely events A and B are collectively exhaustive, what is the probability that event A occurs?
A) 0
B) 0.50
C) 1.00
D) cannot be determined from the information given
Answer: D
20) All the events in the sample space that are not part of the specified event are called
A) simple events.
B) joint events.
C) the sample space.
D) the complement of the event.
Answer: D
21) The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is ________.
A) 0.10
B) 0.33
C) 0.67
D) 0.75
Answer: B
22) The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is ________.
A) 0.10
B) 0.185
C) 0.705
D) 0.90
Answer: A
B:Sales not increase .75
C:Interest rates up .74
D:Interest rates not up .26
A or C .89
P(A and C) = P(A) + P(C) - P(A or C) = 0.25+0.74-0.89 = 0.1
|
|
A:Sales increase |
B:Sales not increase |
|
|
C:Interest rates up |
X |
|
74 |
|
D:Interest rates not up |
|
|
26 |
|
|
25 |
75 |
100 |
23) The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that neither house sales nor interest rates will increase during the next 6 months is ________.
A) 0.11
B) 0.195
C) 0.89
D) 0.90
Answer: A
24) Which of the following about the binomial distribution is NOT a true statement?
A) The probability of the event of interest must be constant from trial to trial.
B) Each outcome is independent of the other.
C) Each outcome may be classified as either "event of interest" or "not event of interest."
D) The random variable of interest is continuous.
Answer: D
25) A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Suppose the mean cost of rats used in lab experiments turned out to be $13.00 per week. Interpret this value.
A) Most of the weeks resulted in rat costs of $13.00.
B) The median cost for the distribution of rat costs is $13.00.
C) The expected or average cost for all weekly rat purchases is $13.00.
D) The rat cost that occurs more often than any other is $13.00.
Answer: C
26) Which of the following about the normal distribution is NOT true?
A) Theoretically, the mean, median, and mode are the same.
B) About 2/3 of the observations fall within ±1 standard deviation from the mean.
C) It is a discrete probability distribution.
D) Its parameters are the mean, μ, and standard deviation, σ.
Answer: C
27) The value of the cumulative standardized normal distribution at Z is 0.8770. The value of Z is ________.
A) 0.18
B) 0.81
C) 1.16
D) 1.47
Answer: C
28) For some value of Z, the value of the cumulative standardized normal distribution is 0.8340. The value of Z is ________.
A) 0.07
B) 0.37
C) 0.97
D) 1.06
Answer: C
29) A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.
Answer: 71.78 years old
30) If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, 75.8% of the college students will take more than how many minutes when trying to find a parking spot in the library parking lot?
A) 2.8 minutes
B) 3.2 minutes
C) 3.4 minutes
D) 4.2 minutes
Answer: A
31) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds) do 89.80% of the weights occur?
Answer: 2.184 pounds
32) True or False: The probability that a standard normal random variable, Z, is below 1.96 is 0.4750.
Answer: FALSE
33) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain less than 100 grams or more than 120 grams of tea leaves?
Answer: 0.6892
34) The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. Approximately 83% of the can will have at least how many grams of tea leaves?
Answer: 86.15 using Excel or 86.25 using Table E.2
35) You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?
Answer: 2.27% or 0.0227
36) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The probability that a randomly selected catfish will weigh between 2.6 and 3.6 pounds is ________.
Answer: 50% or 0.5
37) The owner of a fish market determined that the average weight for a catfish is 3.2 pounds. He also knew that the probability of a randomly selected catfish that would weigh more than 3.8 pounds is 20% and the probability that a randomly selected catfish that would weigh less than 2.8 pounds is 30%. The middle 40% of the catfish will weigh between ________ pounds and ________ pounds.
Answer: 2.8 and 3.6
38) Which of the following sampling methods is a probability sample?
A) convenience sample
B) quota sample
C) stratified sample
D) judgment sample
Answer: C
39) At U.S. Data Corporation's web site, they advertised that "Because of our commitment to quality and our vast amount of industry knowledge and experience, we have grown to be one of America's leading providers of mailing lists, marketing data, sales leads and research data. We maintain databases of information on consumers and businesses nationwide that set industry standards for mission critical currency, reliability, and accuracy." Trying to reach 500 potential donors for their annual phone donation campaign, a local fire department purchased a list of donors from the company. This list is an example of a
A) population.
B) statistic.
C) parameter.
D) frame.
Answer: D
40) To find out the potential impact of a new zoning law on a neighborhood, the legislators conduct a focus group interview by inviting the members of the housing owners association of that neighborhood. This is an example of a
A) systematic sample.
B) simple random sample.
C) judgment sample.
D) cluster sample.
Answer: C
41) ________ results from the exclusion of certain groups of subjects from a population frame.
Answer: Coverage error
42) Coverage error results in a ________.
Answer: selection bias
43) True or False: The professor of a business statistics class wanted to find out the mean amount of time per week her students spent studying for the class. She divided the fifty students on her roster into ten groups starting from the first student on the roster. The first student was randomly selected from the first group. Then every tenth student was selected from the remaining students. This is an example of a cluster sample.
Answer: FALSE
44) True or False: The question: "Have you used any form of illicit drugs over the past two months?" will most likely result in measurement error if the question is answered.
Answer: TRUE
45) If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic
A) unbiased.
B) minimum variance.
C) biased.
D) random.
Answer: A
46) 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: C
47) The distribution of the number of loaves of bread sold per day by a large bakery over the past five years has a mean of 7,750 and a standard deviation of 145 loaves. Suppose a random sample of n = 40 days has been selected. What is the approximate probability that the mean number of loaves sold in the sampled days exceeds 7,895 loaves?
Answer: approximately 0
48) Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. What was the standard error for the sample mean salary?
A) $0.012 million
B) $0.12 million
C) $12 million
D) $1,200.0 million
Answer: B
49) 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 centimeter. 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?
Answer: 0.2710 using Excel or 0.2736 using Table E.2
50) The standard error of the population proportion will become larger
A) as the population proportion approaches 0.
B) as the population proportion approaches 0.50.
C) as the population proportion approaches 1.00.
D) as the sample size increases.
Answer: B
51) 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) 830
C) 920
D) 1,660
Answer: B
52) True or False: The difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.
Answer: TRUE
53) True or False: The width of a confidence interval equals twice the sampling error.
Answer: TRUE
54) True or False: Given a sample mean of 2.1 and a population standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.
Answer: FALSE
55) 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). Based on the interval above, do you believe the mean total compensation of CEOs in the Service industry is more than $3,000,000?
A) Yes, and I am 95% confident of it.
B) Yes, and I am 78% confident of it.
C) I am 95% confident that the mean compensation is $3,000,000.
D) I cannot conclude that the mean exceeds $3,000,000 at the 95% confidence level.
Answer: D
56) 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, = 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: D
57) The county clerk wants to estimate the proportion of voters who will need special election facilities. Suppose a sample of 400 voters was taken. If 150 need special election facilities, calculate an 90% confidence interval for the population proportion.
Answer: 0.3352 to 0.4148
58) A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from ________ to ________.
Answer: 0.063 to 0.117
59) 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: B
60) A confidence interval was used to estimate the proportion of statistics students who are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval above, is the population proportion of females equal to 0.60?
A) No, and we are 90% sure of it.
B) No. The proportion is 54.17%.
C) Maybe. 0.60 is a believable value of the population proportion based on the information above.
D) Yes, and we are 90% sure of it.
Answer: C
61) 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 to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?
A) 99.7%
B) 99.0%
C) 98.0%
D) 95.4%
Answer: A
62) Which of the following would be an appropriate alternative hypothesis?
A) The mean of a population is equal to 55.
B) The mean of a sample is equal to 55.
C) The mean of a population is greater than 55.
D) The mean of a sample is greater than 55.
Answer: C
63) If a test of hypothesis has a Type I error probability (α) of 0.01, it means that
A) if the null hypothesis is true, you don't reject it 1% of the time.
B) if the null hypothesis is true, you reject it 1% of the time.
C) if the null hypothesis is false, you don't reject it 1% of the time.
D) if the null hypothesis is false, you reject it 1% of the time.
Answer: B
64) If a researcher does not reject a false null hypothesis, she has made a ________ error.
Answer: Type II
65) The symbol for the probability of committing a Type I error of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.
Answer: A
66) How many tissues should the Kimberly Clark Corporation package of Kleenex® contain? Researchers determined that 60 tissues is the mean 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 alternative you wanted to test was H1: μ < 60. State the correct rejection region for α = 0.05.
A) Reject H0 if t > 1.6604.
B) Reject H0 if t < -1.6604.
C) Reject H0 if t > 1.9842 or Z < -1.9842.
D) Reject H0 if t < -1.9842.
Answer: B
67) If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed
A) a Type II error.
B) a Type I error.
C) no error.
D) an acceptance error.
Answer: C
68) In testing for the differences between the means of two independent populations, you assume that the two populations each follow a ________ distribution.
Answer: normal
69) True or False: The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.
Answer: FALSE
A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: G = 35 months, SG2 = 900 Metropolis:
M = 50 months, SM2 = 1,050
70) Which of the following represents the relevant hypotheses tested by the real estate company?
A) H0: μG - μM ≥ 0 versus H1: μG - μM < 0
B) H0: μG - μM ≤ 0 versus H1: μG - μM > 0
C) H0: μG - μM = 0 versus H1: μG - μM ≠ 0
D) H0: G -
M ≥ 0 versus H1:
G -
M < 0
Answer: A
71) What is the estimated standard error of the difference between the two sample means?
A) 4.06
B) 5.61
C) 8.01
D) 16.00
Answer: A
72) If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is
A) the Z test.
B) the χ2 test.
C) both A and B
D) neither A nor B.
Answer: C
73) True or False: A test for whether one proportion is higher than the other can be performed using the chi-square distribution.
Answer: FALSE
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery, the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the four procedures, and collects the following numbers of patients from their own records:
They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
74) Referring to the table above, the test will involve ________ degrees of freedom.
Answer: 3
75) Referring to the table above, the overall or mean proportion of clear operations is ________.
Answer: 0.676
76) Referring to the table above, the expected cell frequency for the Procedure A/Clear cell is ________.
Answer: 25.69
77) Referring to Table the table above, the expected cell frequency for the Procedure D/Return cell is ________.
Answer: 5.83
78) Referring to the table above, the critical value of the test is ________.
Answer: 7.815
79) Referring to the table above, the value of the test statistic is ________.
Answer: 7.867
80) True or False: Referring to the table above, the null hypothesis will be rejected.
Answer: TRUE
81) True or False: Referring to the table above, the decision made suggests that the four procedures all have different proportions of clear operations.
Answer: FALSE
82) True or False: Referring to the table above, the decision made suggests that the four procedures do not all have the same proportion of clear operations.
Answer: TRUE
83) The Y-intercept (b0) represents the
A) estimated average Y when X = 0.
B) change in estimated average Y per unit change in X.
C) predicted value of Y.
D) variation around the sample regression line.
Answer: A
84) The strength of the linear relationship between two numerical variables may be measured by the
A) scatter plot.
B) coefficient of correlation.
C) slope.
D) Y-intercept.
Answer: B
85) True or False: When r = -1, it indicates a perfect relationship between X and Y.
Answer: TRUE
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
86) Referring to the table above, which of the following is the correct interpretation for the slope coefficient?
A) For each decrease of 1 thousand downloads, the expected revenue is estimated to increase by $3.7297 thousands.
B) For each increase of 1 thousand downloads, the expected revenue is estimated to increase by $3.7297 thousands.
C) For each decrease of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.
D) For each increase of 1 thousand dollars in expected revenue, the expected number of downloads is estimated to increase by 3.7297 thousands.
Answer: B
87) Referring to the table above, predict the revenue when the number of downloads is 30 thousands.
Answer: $16.8296 thousands
88) Referring to the table above, which of the following is the correct interpretation for the coefficient of determination?
A) 74.67% of the variation in revenue can be explained by the variation in the number of downloads.
B) 75.54% of the variation in revenue can be explained by the variation in the number of downloads.
C) 74.67% of the variation in the number of downloads can be explained by the variation in revenue.
D) 75.54% of the variation in the number of downloads can be explained by the variation in revenue.
Answer: B
89) Referring to the table above, what is the standard error of estimate?
Answer: $44.4765 thousands
