Q1. Which of the following is true regarding the sampling distribution of the mean for a large sample size?
a. It has the same shape, mean, and standard deviation as the population.
b. It has a normal distribution with the same mean and standard deviation as the population.
c. It has the same shape and mean as the population, but has a smaller standard deviation.
d. It has a normal distribution with the same mean as the population but with a smaller standard deviation.
Q2. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that annual household income is over $25,000 if the residents of a household do not own 2 cars is:
a. 0.12
b. 0.18
c. 0.40
d. 0.55
Q3. The collection and summarization of the socioeconomic and physical characteristics of the employees of a particular firm is an example of:
a. inferential statistics.
b. descriptive statistics.
c. a parameter.
d. a statistic.
Q4. 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%
Q5. Referring to the histogram, how many graduating seniors attended the luncheon?
a. 4
b. 152
c. 275
d. 388
Q6. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.
| Time (in Minutes) | Relative Frequency |
| 0 but less than 5 | 0.37 |
| 5 but less than 10 | 0.22 |
| 10 but less than 15 | 0.15 |
| 15 but less than 20 | 0.10 |
| 20 but less than 25 | 0.07 |
| 25 but less than 30 | 0.07 |
| 30 or more | 0.02 |
Referring to the table, if 10 calls lasted 30 minutes or more, how many calls lasted less than 5 minutes?
a. 10
b. 185
c. 295
d. 500
Q7. The collection of all possible events is called:
a. a simple probability.
b. a sample space.
c. a joint probability.
d. the null set.
Q8. A lab orders 100 rats a week for each of the 52 weeks in the year for experiments that the lab conducts. Prices for 100 rats follow the following distribution:
| Price: | $10.00 | $12.50 | $15.00 |
| Probability: | 0.35 | 0.40 | 0.25 |
How much should the lab budget for next year’s rat orders be, assuming this distribution does not change?
a. $520
b. $637
c. $650
d. $780
Q9. 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%
Q10. Since a _______ is not a randomly selected probability sample, there is no way to know how well it represents the overall population.
a. simple random sample
b. quota sample
c. stratified sample
d. cluster sample
Q11. A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled.
a. The 250 randomly selected adult American pine trees in the forest.
b. The 25,000 adult American pine trees in the forest.
c. All the adult American pine trees taller than 60 feet in the world.
d. All American pine trees, of any age, in the forest.
Q12. A population frame for a survey contains a listing of 72,345 names. Using a table of random numbers, how many digits will the code numbers for each member of your population contain?
a. 3
b. 4
c. 5
d. 6
Q13. The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the portion of students at her university who visited campus bars every weekend. Her advisor took a random sample of 250 students. The portion of students in the sample who visited campus bars every weekend is an example of a __________.
a. categorical random variable
b. discrete random variable
c. parameter
d. statistic
Q14. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.
| Time (in Minutes) | Relative Frequency |
| 0 but less than 5 | 0.37 |
| 5 but less than 10 | 0.22 |
| 10 but less than 15 | 0.15 |
| 15 but less than 20 | 0.10 |
| 20 but less than 25 | 0.07 |
| 25 but less than 30 | 0.07 |
| 30 or more | 0.02 |
Referring to Table 2-5, if 100 calls were randomly sampled, how many calls lasted 15 minutes or longer?
a. 10
b. 14
c. 26
d. 74
Q15. 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.
Q16. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25,000 is 80%. Of the households surveyed, 60% had incomes over $25,000 and 70% had 2 cars. The probability that the residents of a household do not own 2 cars and have an income over $25,000 a year is:
a. 0.12
b. 0.18
c. 0.22
d. 0.48
Q17. If two events are mutually exclusive and collectively exhaustive, 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.
Q18. Why is the Central Limit Theorem so important to the study of sampling distributions?
a. It allows us to disregard the size of the sample selected when the population is not normal.
b. It allows us to disregard the shape of the sampling distribution when the size of the population is large.
c. It allows us to disregard the size of the population we are sampling from.
d. It allows us to disregard the shape of the population whennis large.
Q19. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.
| Did Well on Midterm | Did Poorly on Midterm | |
| Studying for Exam | 80 | 20 |
| Went Bar Hopping | 30 | 70 |
Referring to the table, of those who did well on the midterm in the sample, _______ percent of them went bar hopping the weekend before the midterm.
a. 15
b. 27.27
c. 30
d. 50
Q20. Tim was planning for a meeting with his boss to discuss a raise in his annual salary. In preparation, he wanted to use the Consumer Price Index to determine the percentage increase in his salary in terms of real income over the last three years. Which method of data collection was involved when he used the Consumer Price Index?
a. Published sources
b. Experimentation
c. Surveying
d. Observation
Q21. A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below.
| Stem | Leaves |
| 3 | 24 |
| 4 | 3478999 |
| 5 | 112345 |
| 6 | 12566 |
| 7 | 1 |
| 8 | |
| 9 | 2 |
Referring to the table, what percentage of the respondents rated overall television quality with a rating between 50 and 75?
a. 0.11
b. 0.40
c. 0.44
d. 0.56
Q22. The process of using sample statistics to draw conclusions about true population parameters is called:
a. statistical inference.
b. the scientific method.
c. sampling.
d. descriptive statistics.
Q23. 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.
Q24. Which of the following is most likely a parameter as opposed to a statistic?
a. The average score of the first five students completing an assignment.
b. The proportion of females registered to vote in a county.
c. The average height of people randomly selected from a database.
d. The proportion of trucks stopped yesterday that were cited for bad brakes.
Q25. Selection of raffle tickets from a large bowl is an example of:
a. sampling with replacement.
b. sampling without replacement.
c. subjective probability.
d. None of the above.
Q26. The portfolio expected return of two investments
a. will be higher when the covariance is zero.
b. will be higher when the covariance is negative.
c. will be higher when the covariance is positive.
d. does not depend on the covariance.
Q27. Given the numbers: 1, 3, 5, 7, 8 what are the average and the median?
a. Average = 4.8; Median = 5.0
b. Average = 5.0; Median = 5.0
c. Average = 4.8; Median = 4.8
d. Average = 5.0; Median = 4.8
Q28. The employees of a company were surveyed on questions regarding their educational background and marital status. 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 is single or has a college degree is:
a. 0.10
b. 0.25
c. 0.667
d. 0.733
Q29. A catalog company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product. The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 3 minutes. What proportion of customers having to hold more than 1.5 minutes will hang up before placing an order?
a. 0.86466
b. 0.60653
c. 0.39347
d. 0.13534
Q30. The following are the durations in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier.
| Time (in Minutes) | Relative Frequency |
| 0 but less than 5 | 0.37 |
| 5 but less than 10 | 0.22 |
| 10 but less than 15 | 0.15 |
| 15 but less than 20 | 0.10 |
| 20 but less than 25 | 0.07 |
| 25 but less than 30 | 0.07 |
| 30 or more | 0.02 |
Referring to the table, what is the width of each class?
a. 1 minute
b. 5 minutes
c. 2%
d. 100%
Q31. The probability that
- house sales will increase in the next 6 months is estimated to be 0.25.
- the interest rates on housing loans will go up in the same period is estimated to be 0.74
- house sales or interest rates will go up during the next 6 months is estimated to be 0.89
The probability that house sales will increase but interest rates will not during the next 6 months is:
a. 0.065
b. 0.15
c. 0.51
d. 0.89
Q32. Which of the mean, median, mode, and geometric mean are resistant measures of central tendency?
a. The mean and median.
b. The median and mode.
c. The mode and geometric mean.
d. The mean and mode.
Q33. The probability that
- house sales will increase in the next 6 months is estimated to be 0.25
- the interest rates on housing loans will go up in the same period is estimated to be 0.74
- 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
Q34. Which of the following statistics is not a measure of central tendency?
a. Mean.
b. Median.
c. Mode.
d. Q3.
Q35. The width of each bar in a histogram corresponds to the:
a. differences between the boundaries of the class.
b. number of observations in each class.
c. midpoint of each class.
d. percentage of observations in each class.
Q36. In left-skewed distributions, which of the following is the correct statement?
a. The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3.
b. The distance from the smallest observation to Q1 is larger than the distance from Q3 to the largest observation.
c. The distance from the smallest observation to Q2 is smaller than the distance from Q2 to the largest observation.
d. The distance from Q1 to Q3 is twice the distance from Q1 to Q2.
Q37. The Central Limit Theorem is important in statistics because:
a. for a largen, it says the population is approximately normal.
b. for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size.
c. for a largen, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population.
d. for any sized sample, it says the sampling distribution of the sample mean is approximately normal.
Q38. A sample of 200 students at a Big-Ten university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result.
| Did Well on the midterm | Did Poorly on Midterm | |
| Studying for Exam | 80 | 20 |
| Went Bar Hopping | 30 | 70 |
Referring to the table, _______ percent of the students in the sample went bar hopping the weekend before the midterm and did well on the midterm.
a. 15
b. 27.27
c. 30
d. 50
Q39. Which of the following statements about the median is not true?
a. It is more affected by extreme values than the mean.
b. It is a measure of central tendency.
c. It is equal to Q2.
d. It is equal to the mode in bell-shaped “normal” distributions.
Q40. A confidence interval was used to estimate the proportion of statistics students that 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.
Q1. The sample correlation coefficient between X and Y is 0.375. It has been found out that the p-value is 0.256 when testing H0: ρ = 0 against the two-sided alternative H1: ρ ≠ 0. To test H0: ρ = 0 against the one-sided alternative H1: ρ > 0 at a significance level of 0.193, the p-value is
a. 0.256/2
b. 0.256
c. 1 – 0.256
d. 1 – 0.256/2
Q2. A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.
| Size | Mean | Std Dev | |
| Females | 18 | 48,266.7 | 13,577.63 |
| Males | 12 | 55,000 | 11,741.29 |
| Std Error = 4,764.82 | |||
| Means Diff = -6,733.3 | |||
| Z = -1.4528 2-tailed p value = 0.1463 | |||
| T = -1.4221 2-tailed p value = 0.1574 |
Referring to the table, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
a. Both populations of salaries (male and female) must have approximate normal distributions.
b. The population variances are approximately equal.
c. The samples were randomly and independently selected.
d. All of the above assumptions were necessary.
Q3. The Y-intercept (b0) represents the:
a. predicted value of 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.
Q4. A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes. The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent samples were selected from the 2 neighborhoods from last year’s homes sales, 8 from each of the 2 neighborhoods. Identify the nonparametric method that would be used to analyze the data.
a. the Wilcoxon Signed-Ranks Test, using the test statistic Z
b. the Wilcoxon Signed-Ranks Test, using the test statistic W
c. the Wilcoxon Rank Sum Test, using the test statistic T1
d. the Wilcoxon Rank Sum Test, using the test statistic Z
Q5. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:
a. -4.12
b. -2.33
c. -1.86
d. -0.07
Q6. A realtor wants to compare the average sales-to-appraisal ratios of residential properties sold in four neighborhoods (W, X, Y, and Z). Four properties are randomly selected from each neighborhood and the ratios recorded for each, as shown below.
W: 1.2, 1.1, 0.9, 0.4
X: 2.5, 2.1, 1.9, 1.6
Y: 1.0, 1.5, 1.1, 1.3
Z: 0.8, 1.3, 1.1, 0.7
Interpret the results of the analysis summarized in the following table:
| Source | df | SS | MS | F | PR > F |
| Neighborhoods | 2.97 | 0.990 | 8.31 | 0.0260 | |
| Error | 12 | ||||
| Total | 4.40 |
Referring to the table, the within group mean squares is
a. 0.119
b. 0.990
c. 1.109
d. 8.31
Q7. If a group of independent variables are not significant individually but are significant as a group at a specified level of significance, this is most likely due to:
a. autocorrelation.
b. the presence of dummy variables.
c. the absence of dummy variables.
d. collinearity.
Q8. In a multiple regression model, the adjusted r2
a. cannot be negative.
b. can sometimes be negative.
c. can sometimes be greater than +1.
d. has to fall between 0 and +1.
Q9. Why would you use the Tukey-Kramer procedure?
a. To test for normality.
b. To test for homogeneity of variance.
c. To test independence of errors.
d. To test for differences in pairwise means.
Q10. A campus researcher wanted to investigate the factors that affect visitor travel time in a complex, multilevel building on campus. Specifically, he wanted to determine whether different building signs (building maps versus wall signage) affect the total amount of time visitors require to reach their destination and whether that time depends on whether the starting location is inside or outside the building. Three subjects were assigned to each of the combinations of signs and starting locations, and travel time in seconds from beginning to destination was recorded. How should the data be analyzed?
| Starting Room | ||
| Interior | Exterior | |
| Wall Signs | 141 | 224 |
| 119 | 339 | |
| 238 | 139 | |
| Map | 85 | 226 |
| 94 | 129 | |
| 126 | 130 |
a. Completely randomized design
b. Randomized block design
c. 2 x 2 factorial design
d. Kruskal-Wallis rank test
Q11. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is
Yi = ß0 + ß1x1i + ß2x2i + ß3x3i + ei
where
Y is the price per hour
x1 is a numerical variable = the number of blocks to the quadrangle
(Note that if x1 is less than 2, then the meter is on campus; if x1 is less than 3, then the meter is downtown)
x2 is a dummy variable = 1 if inside downtown and off campus, 0 otherwise
x3 is a dummy variable = 1 if outside downtown and off campus, 0 otherwise
The following Excel results are obtained.
| Regression Statistics | |
| Multiple R | 9.9659 |
| R Square | 0.9331 |
| Adjusted R Square | 0.9294 |
| Standard Error | 0.0327 |
| Observations | 58 |
| ANOVA | df | SS | MS | F | Signif F |
| Regression | 3 | 0.8094 | 0.2698 | 251.1995 | 1.0964E-31 |
| Residual | 54 | 0.0580 | 0.0010 | ||
| Total | 57 | 0.8675 |
| Coeff | StdError | t Stat | P-value | |
| Intercept | 0.5118 | 0.0136 | 37.4675 | 2.4904 |
| X1 | -0.0045 | 0.0034 | -1.3275 | 0.1898 |
| X2 | -0.2392 | 0.0123 | -19.3942 | 5.3581E-26 |
| X3 | -0.0002 | 0.0123 | -0.0214 | 0.9829 |
Referring to the tables, predict the meter rate per hour if one parks outside of downtown and off campus, 3 blocks from the quad.
a. $-0.0139
b. $0.2589
c. $0.2604
d. $0.4981
Q12. If we use the chi-squared method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:
a. 3
b. 4
c. 5
d. 1
Q13. An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). The Microsoft Excel output of this regression is partially reproduced below.
SUMMARY OUTPUT
| Regression Statistics | |
| Multiple R | 0.991 |
| R Square | 0.982 |
| Adjusted R Square | 0.976 |
| Standard Error | 0.299 |
| Observations | 10 |
| ANOVA | df | SS | MS | F | Signif F |
| Regression | 2 | 33.4163 | 16.7082 | 186.325 | 0.0001 |
| Residual | 7 | 0.6277 | 0.0897 | ||
| Total | 9 | 34.0440 |
| Coeff | StdError | t Stat | P-value | |
| Intercept | -0.0861 | 0.5674 | -0.152 | 0.8837 |
| GDP | 0.7654 | 0.0574 | 13.340 | 0.0001 |
| Price | -0.0006 | 0.0028 | -0.219 | 0.8330 |
Referring to the tables, one economy in the sample had an aggregate consumption level of $4 billion, a GDP of $6 billion, and an aggregate price level of 200. What is the residual for this data point?
a. $4.39 billion
b. $0.39 billion
c. -$0.39 billion
d. -$1.33 billion
Q14. Testing for the existence of correlation is equivalent to
a. testing for the existence of the slope (β1).
b. testing for the existence of the Y-intercept (β0).
c. the confidence interval estimate for predicting Y.
d. testing for the existence of the slope (β10).
Q15. As a business statistics project, a student examined the factors that determine parking meter rates throughout the campus and downtown area. The campus is a group of buildings located in the center of downtown, with an open central quadrangle. Data were collected for the price of parking per hour and the number of blocks to the quadrangle. In addition, two dummy variables were coded to indicate the location of the parking meter (See below). The population regression model hypothesized is
Yi = ß0 + ß1x1i + ß2x2i + ß3x3i + ei
where
Y is the price per hour
x1 is a numerical variable = the number of blocks to the quadrangle
(Note that if x1 is less than 2, then the meter is on campus; if x1 is less than 3, then the meter is downtown)
x2 is a dummy variable = 1 if inside downtown and off campus, 0 otherwise
x3 is a dummy variable = 1 if outside downtown and off campus, 0 otherwise
The following Excel results are obtained.
| Regression Statistics | |
| Multiple R | 9.9659 |
| R Square | 0.9331 |
| Adjusted R Square | 0.9294 |
| Standard Error | 0.0327 |
| Observations | 58 |
| ANOVA | df | SS | MS | F | Signif F |
| Regression | 3 | 0.8094 | 0.2698 | 251.1995 | 1.0964E-31 |
| Residual | 54 | 0.0580 | 0.0010 | ||
| Total | 57 | 0.8675 |
| Coeff | StdError | t Stat | P-value | |
| Intercept | 0.5118 | 0.0136 | 37.4675 | 2.4904 |
| X1 | -0.0045 | 0.0034 | -1.3275 | 0.1898 |
| X2 | -0.2392 | 0.0123 | -19.3942 | 5.3581E-26 |
| X3 | -0.0002 | 0.0123 | -0.0214 | 0.9829 |
Referring to the tables, if one is already outside of downtown and off campus but decides to park an additional 3 blocks from the quadrangle, the estimated average parking meter rate will:
a. decrease by 0.0045.
b. decrease by 0.0135.
c. decrease by 0.0139.
d. decrease by 0.4979.
Q16. The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.
Hypothesized Difference0
Level of Significance 0.05
Group 1
Number of Successes163
Sample Size227
Group 2
Number of Successes154
Sample Size262
Group 1 Proportion0.718061674
Group 2 Proportion0.58778626
Difference in Two Proportions 0.130275414
Average Proportion0.648261759
Test Statistic3.00875353
Two-Tailed Test
Lower Critical Value -1.959961082
Upper Critical Value 1.959961082
p-Value 0.002623357
Referring to the data above, if you want to test the claim that “Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2),” the p-value of the test will be
a. 0.00262
b. 0.00262/2
c. 2*(0.00262)
d. 1 – (0.00262/2)
Q17. A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The builder randomly selected 50 families and ran the µltiple regression. Microsoft Excel output is provided below:
SUMMARY OUTPUT
| Regression Statistics | |
| Multiple R | 0.865 |
| R Square | 0.748 |
| Adjusted R Square | 0.726 |
| Standard Error | 5.195 |
| Observations | 50 |
| ANOVA | df | SS | MS | F | Signif F |
| Regression | 3605.7736 | 901.4434 | 0.0001 | ||
| Residual | 1214.2264 | 26.9828 | |||
| Total | 49 | 4820.0000 |
| Coeff | StdError | t Stat | P-value | |
| Intercept | -1.6335 | 5.8078 | -0.281 | 0.7798 |
| Income | 0.4485 | 0.1137 | 3.9545 | 0.0003 |
| Size | 4.2615 | 0.8062 | 5.286 | 0.0001 |
| School | -0.6517 | 0.4319 | -1.509 | 0.1383 |
Referring to the tables, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square
