STAT 210 Final!
An investor has a $100,000 portfolio of which $75,000 has been invested in Stock A and the remainder in Stock B. Other characteristics of the portfolio are shown in the accompanying table. The standard deviation of the portfolio is____. 9.39(%) 14.19(%) 88.23(%)^2 201.41(%)^2
9.39(%)
Thirty students at Eastside High School took the SAT on the same Saturday. Their raw scores are given next. Consider a frequency distribution of the data that groups the data in classes of 1400 up to 1600, 1600 up to 1800 , 1800 up to 2000 and so on. What percent of students scored less than 2200? 10% 20% 80% 90%
90%
Use the following data to construct a scatterplot. What type of relationship is implied? No relationship A positive relationship A negative relationship Not enough information to answer
A negative relationship
A Monster.com pool of 3,057 individuals asked: "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. The 99% confidence interval for the proportion of people who plan a one-week or two-week vacation this summer is______. [0.563, 0.603] [0.557, 0.597] [0.563, 0.597] [0.557, 0.603]
[0.557, 0.603]
Given a sample mean of 12.5—drawn from a normal population, a sample of size 25, and a sample variance of 2.4—find a 99% confidence interval for the population mean. [11.7019, 13.2981] [11.1574, 13.8426] [11.6334, 13.3666] [11.7279, 13.2721]
[11.6334, 13.3666]
The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure, and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 99% confidence interval for the mean duration of the foreclosure process in Boston. [126.2730, 539.2270] [259.7486, 405.7514] [279.0056, 386.4944] [291.8600, 373.6400]
[259.7486, 405.7514]
A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.23,7.89,8.14,8.25,8.30, and 7.95 hours before burning out in each of the tests. Assuming the battery duration is normally distributed, construct a 95% confidence interval for the mean battery life in the new model. [7.9489, 8.3045] [7.9575, 8.2959] [7.9873, 8.2661] [7.9912, 8.2622]
[7.9489, 8.3045]
Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election. [0.4534, 0.5666] [0.4625, 0.5575] [0.5084, 0.5116] [0.5086, 0.5114]
[0.4534, 0.5666]
Amounts spent by a sample of 50 customers at a retail store are summarized in the following relative frequency distribution. The mean amount spent by customers is the closest to_____. $0.36 $18.00 $20.00 $25.00
$18.00
Amounts spent by a sample of 200 customers at a retail store are summarized in the following relative frequency distribution. The mean amount spent by customers is the closest to _____. $17.50 $20.00 $22.50 $50.00
$22.50
Professors at a local university earn an average salary of $80,000 with a standard deviation of $6,000. With the beginning of the next academic year, all professors will get a 2% raise. What will be the average and the standard deviation of their new salaries? $80,000 and $6,120 $81,600 and $6,000 $81,600 and $6,120 $82,000 and $6,200
$81,600 and $6,120
The covariance between the returns of A and B is -0.112.The standard deviation of the rates of return is 0.26 for stock A and 0.81 for stock B. The correlation of the rates of return between A and B is the closest to _____. -1.88 -0.53 0.53 1.88
-0.53
The time to complete the construction of a soapbox derby car is normally distributed with a mean of three hours and a standard deviation of one hour. Find the probability that it would take exactly 3.7 hours to construct a soapbox derby car. 0.0000 0.5000 0.7580 0.2420
0.0000
Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. Professor Elderman offers his class of 36 a pizza party if the class average is above 80. What is the probability that he will have to deliver on his promise? 0.0228 0.3707 0.6293 0.9772
0.0228
Suppose the life of a particular brand of laptop battery is normally distributed with a mean of 8 hours and a standard deviation of 0.6 hours. What is the probability that the battery will last more than 9 hours before running out of power? 0.0475 0.4525 0.9525 1.6667
0.0475
According to geologists, the San Francisco Bay Area experiences five earthquakes with a magnitude of 6.5 or greater every 100 years. What is the probability that one or more earthquakes with a magnitude of 6.5 or greater will strike the San Francisco Bay Area in the next year? 0.0488 0.1353 0.4878 0.9512
0.0488
A local company makes snack-size bags of potato chips. Each day, the company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the amount placed in each of the 400 bags is normally distributed and has a standard deviation of 0.1 ounce. What is the probability that a sample of 40 bags has an average weight of at least 2.02 ounces? 0.0150 0.0918 0.1038 0.4207
0.0918
According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patients will get a correct diagnosis for extreme longevity? 0.1422 0.0722 0.2214 0.0207
0.1422
A bank manager estimates that an average of two customers enter the tellers' queue every five minutes. Assume that the number of customers that enter the tellers' queue is Poisson distributed. What is the probability that exactly three customers enter the queue in a randomly selected five-minute period? 0.0902 0.1804 0.2240 0.2707
0.1804
The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What is the probability that between 60% and 62.5% of those surveyed are members of the labor force? 0.0243 0.1931 0.2005 0.3936
0.1931
Let P(AnB) = 0.3, and P(A n B^c) =0.15, and P(A^c n B) = 0.35. Compute P(A^c n B^c). 0.20 0.50 0.65 0.70
0.20
The average time between trades for a high-frequency trading investment firm is 40 seconds. Assume the time between trades is exponentially distributed. What is the probability that the time between trades for a randomly selected trade and the one proceeding it is more than a minute? 0.2231 0.4869 0.5134 0.7769
0.2231
For a particular clothing store, a marketing firm finds that 16% of $10-off coupons delivered by mail are redeemed. Suppose six customers are randomly selected and are mailed $10-off coupons. What is the probability that at least two of the customers redeem the coupon? 0.2472 0.3513 0.4015 0.7528
0.2472
Suppose a baseball team has 14 players on the roster who are not members of the pitching staff. Of those 14 players, assume that three have recently taken a performance-enhancing drug. Suppose the league decides to randomly test five members of the team. What is the probability that exactly two of the tested players are found to have taken a performance-enhancing drug? 0.2308 0.2473 0.4945 0.7692
0.2473
Suppose that 60% of the students do homework regularly. It is also known that 80% of students who had been doing homework regularly end up doing well in the course. Only 20% of students who had not been doing homework regularly end up doing well in the course. What is the probability that a student does well in the course? 0.080 0.480 0.560 0.857
0.560
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000 dollars. What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000? 0.5899 0.7486 0.8413 0.9048
0.5899
Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. If during a typical week Susan bowls 16 games, what is the probability that her average score for the week is between 220 and 228? 0.0618 0.2390 0.7594 0.8212
0.7594
A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is between 0.20 and 0.35 is 0.1867 0.7766 0.8133 0.9633
0.7766
According to a study by the Centers for Disease Control and Prevention, about 33% of U.S. births are Caesarean deliveries. Suppose seven expectant mothers are randomly selected. What is the probability that at least one of the expectant mothers will have a Caesarean delivery? 0.0606 0.2090 0.9394 0.9742
0.9394
A statistics professor works tirelessly to catch students cheating on his exams. He has particular routes for his teaching assistants to patrol, an elevated chair to ensure an unobstructed view of all students, and even a video recording of the exam in case additional evidence needs to be collected. He estimates that he catches 95% of students who cheat in his class, but 1% of the time that he accuses a student of cheating he is actually incorrect. Consider the null hypothesis, "the student is not cheating." What is the probability of a Type I error? 1% 5% 95% 99%
1%
The manager at a water park constructed the following frequency distribution to summarize attendance in July and August. What of the following is the most likely attendance range? 2,000 up to 2,500 1,750 up to 2,000 1,000 up to 1,750 1,250 up to 1,750
1,000 up to 1,750
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup. The test statistic for this hypothesis would be _______. 1.35 1.05 1.25 1.01
1.01
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. At the 5% significance level, the critical value would be ______. 1.960 1.645 2.030 1.740
1.740
The following frequency distribution represents the number of hours studied per week by a sample of 50 students. The standard deviation of the number of hours studied is _____. 1.89 2.79 3.50 3.56
1.89
The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation? 10.7688 12.8309 115.9671 164.6326
10.7688
Let X be normally distributed with mean µ = 250 and standard deviation σ = 80. Find the value x such that P(X ≤ x) = 0.0606. -1.55 1.55 126 374
126
You are planning a May camping trip to Denali National Park in Alaska and want to make sure your sleeping bag is warm enough. The average low temperature in the park for May follows a normal distribution with a mean of 32°F and a standard deviation of 8°F. Above what temperature must the sleeping bag be suited such that the temperature will be too cold only 5% of the time? -1.645 1.645 18.84 45.16
18.84
Let X be normally distributed with mean µ = 25 and standard deviation σ = 5. Find the value x such that P(X ≥ x) = 0.1736. -0.94 0.94 20.30 29.70
29.70
The director of graduate admissions is analyzing the relationship between scores in the Graduate Record Examination(GRE) and student performance in graduate school, as measured by a student's GPA. The table below shows a sample of 10 students. The covariance is _____. 53.5 51.75 57.5 58.75
57.5
Automobiles traveling on a road with a posted speed limit of 65 miles per hour are checked for speed by a state police radar system. The following is a frequency distribution of speeds. The standard deviation of this distribution is the closest to _____. 5.35 6.81 9.54 10.25
6.81
An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year. The analyst has developed a ratio to help forecast this decline. If the company is headed for a decline, there is a 90% chance that this ratio will be negative. If the company is not headed for a decline, there is only a 10% chance that the ratio will be negative. The analyst randomly selects a company with a negative ratio. Based on Bayes's theorem, the posterior probability that the company will experience a decline is 18% 26% 44% 69%
69%
The following frequency distribution shows the frequency of the asking price, in thousands of dollars, for current homes on the market in a particular city. What percentage of houses has an asking price under $550,000? 50.5% 69.1% 89.1% 95.0%
89.1%
Sampling is used heavily in manufacturing and service settings to ensure high-quality products. In which of the following areas would sampling be inappropriate? Computer assembly Custom cabinet making Cell phone manufacturing Technical support by phone
Custom cabinet making
Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. Which of the following should be used to develop the null and alternative hypotheses to test this claim? Ho: pbar = 0.50, HA: pbar =/ 0.50 Ho: p >= 0.47, HA: p < 0.47 Ho: p <= 0.47, HA: p > 0.47 Ho: μ >= 72, HA: μ < 72
Ho: p <= 0.47, HA: p > 0.47
The Institute of Education Sciences measures the high school dropout rate as the percentage of 16-through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. When testing whether the dropout rate has decreased, the appropriate hypotheses are ______. Ho: p <= 0.065, HA: p > 0.065 Ho: pbar >= 0.065, HA: pbar < 0.065 Ho: p = 0.081, HA: p =/ 0.081 Ho: p >= 0.081, HA: p < 0.081
Ho: p >= 0.081, HA: p < 0.081
A sample of 1,400 American households was asked if they planned to buy a new car next year. Of the respondents, 34% indicated they planned to buy a new car next year. Construct a 90% confidence interval of the proportion of American households who expect to buy a new car next year. [0.3152, 0.3648] [0.3191, 0.3609] [0.3394, 0.3406] [0.3354, 0.3446]
[0.3191, 0.3609]
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. If this is to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network receives 827 responses, of which 428 indicate they would like to see the new show in the lineup. Which of the following is an appropriate hypotheses to test if the television network should give its newest show a spot during prime time at night? Ho:p < 0.50, HA:p ≥ 0.50 Ho:p ≥ 0.50, HA:p < 0.50 Ho:p ≤ 0.50, HA:p > 0.50 Ho:p = 0.50, HA:p ≠ 0.50
Ho:p ≤ 0.50, HA:p > 0.50
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 10.8 pounds with a standard deviation of 2.4 pounds. Which of the following is an appropriate hypotheses to test the advertisement's claim? Ho:μ < 10, HA:μ ≥ 10 Ho:μ ≥ 10,HA:μ < 10 Ho:μ ≤ 10,HA:μ > 10 Ho:μ = 10,HA:μ ≠ 10
Ho:μ ≤ 10,HA:μ > 10
The table below gives statistics relating to a hypothetical 10-year record of two portfolios. Assume other statistics relating to these portfolios are the same and the risk-free rate is 3.5%. Using the coefficient of variation and the Sharpe ratio, the fund that is preferred in terms of relative risk and return per unit of risk is:_______. Using the coefficient of variation and the Sharpe ratio, the fund that is preferred in terms of relative risk and return per unit of risk is _______. Portfolio A because it has a higher coefficient of variation and a lower Sharpe ratio. Portfolio A because it has a lower coefficient of variation and a higher Sharpe ratio. Portfolio B because it has a higher coefficient of variation and a lower Sharpe ratio. Portfolio B because it has a lower coefficient of variation and a higher sharpe ratio.
Portfolio A because it has a lower coefficient of variation and a higher Sharpe ratio.
Students who graduated from college in 2010 owed an average of $25,250 in student loans. An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their average debt is $27,500 with a standard deviation of $9,120. Use 90% confidence interval. Which of the following conclusion is correct? The average debt decreased. The average debt increased. The average debt has not changed. There is not enough information.
The average debt has not changed.
A manager at a temp agency believes that one of the agency's recruiters has unorthodox methods and claims that the wages the recruiter secures for its temps differ from the agency's average wage of $12 per hour. The agency takes a random sample of 49 recent contracts the recruiter secured and finds an average wage of $11.25 per hour and a standard deviation of $2.25 per hour. Does the evidence support the agency's claim at the 5% significance level? Yes, because the p-value is greater than α, the claim is supported. No, because the p-value is not greater than α, the claim is not supported. Yes, because the value of the test statistic is less than the critical value, the claim is supported. No, because the value of the test statistic is greater than the critical value, the claim is not supported.
Yes, because the value of the test statistic is less than the critical value, the claim is supported.
Suppose taxi fare from Logan Airport to downtown Boston is known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. What is a 95% confidence interval for the population mean taxi fare? [$17.4571, $27.2571] [$20.5051, $24.2091] [$20.8027, $23.9115] [$21.6571, $23.0571]
[$20.5051, $24.2091]
A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% of respondents indicating the country was "an enemy". Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy." [0.2013, 0.2587] [0.2116, 0.2484] [0.2146, 0.2454] [0.2208, 0.2392]
[0.2116, 0.2484]
An analyst studies a data set of the 2011 year-end book value per share for all companies listed on the New York Stock Exchange. This data set is best described as: timeseries data cross-sectional data neither timeseries nor cross-sectional data a combination of timeseries and cross-sectional data
cross-sectional data
To test if the mean returns on a major index have changed from the historic monthly average of 1.2%, a sample of 36 recent monthly returns is used to calculate the value of the relevant tdf test statistic. At the 5% level of significance, we reject the null hypothesis if this value is ____________. greater than 1.69 greater than 1.645 greater than 1.96 or less than -1.96 greater than 2.03 or less than -2.03
greater than 2.03 or less than -2.03
Find the minimum sample size when we want to construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported candidate B and 14 supported candidate C. The desired margin of error is 0.06. n = 173 n = 174 n = 245 n = 246
n = 246
The covariance between the returns on two assets is negative. This occurs when... the variance of one asset has a negative linear relationship with the variance of the other asset the standard deviation of one asset has a positive linear relationship with the standard deviation of the other asset on average, the return on one asset is below its expected value and the return on the other asset is above its expected value on average, the return on one asset is below its expected value and the return on the other asset is below its expected value
on average, the return on one asset is below its expected value and the return on the other asset is above its expected value
The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. At a 5% significance level, the decision is to ________. reject Ho; we can conclude that the high school dropout rate has decreased reject Ho; we cannot conclude that the high school dropout rate has decreased do not reject Ho; we can conclude that the high school dropout rate has decreased do not reject Ho; we cannot conclude that the high school dropout rate has decreased
reject Ho; we can conclude that the high school dropout rate has decreased
A recent report claimed that Americans are retiring later in life (U.S. News & World Report, August 17, 2011). An economist wishes to determine if the mean retirement age has increased from 62. To conduct the relevant test, she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t37 = 1.92. With α = 0.05, she ____________. rejects the null hypothesis and concludes that the mean retirement age has increased rejects the null hypothesis and concludes that the mean retirement age has not increased does not reject the null hypothesis and does not conclude that the mean retirement age has changed does not reject the null hypothesis and does not conclude that the mean retirement age has increased
rejects the null hypothesis and concludes that the mean retirement age has increased
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. the franchiser builds on an acceptable site the franchiser builds on an unacceptable site the franchiser does not build on an acceptable site the franchiser does not build on an unacceptable site
the franchiser builds on an unacceptable site
According to a report in USAToday (February 1, 2012), more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population proportion, then the resulting margin of error will increase and the risk of reporting an incorrect interval will increase the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease
the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
The Institute of Education Sciences measures the high school dropout rate as the percentage of 16- through 24-year-olds who are not enrolled in school and have not earned a high school credential. In 2009, the high school dropout rate was 8.1%. A polling company recently took a survey of 1,000 people between the ages of 16 and 24 and found that 6.5% of them are high school dropouts. The polling company would like to determine whether the dropout rate has decreased. The value of the test statistic is _____. z = -2.052 z = -1.854 z = 1.854 z = 2.052
z = -1.854
Vermont-based Green Mountain Coffee Roasters dominates the market for single-serve coffee in the United States, with its subsidiary Keurig accounting for approximately 70% of sales ("Rivals Try to Loosen Keurig's Grip on Single-Serve Coffee Market," Chicago Tribune, February 26, 2011). But Keurig's patent on K-cups, the plastic pods used to brew the coffee, is expected to expire in 2012, allowing other companies to better compete. Suppose a potential competitor has been conducting blind taste tests on its blend and finds that 47% of consumers strongly prefer its French Roast to that of Green Mountain Coffee Roasters. After tweaking its recipe, the competitor conducts a test with 144 tasters, of which 72 prefer its blend. The competitor claims that its new blend is preferred by more than 47% of consumers to Green Mountain Coffee Roasters' French Roast. What is the value of the appropriate test statistic to test this claim? t143 = 0.721 z = 0.721 t143 = 1.96 z = 1.96
z = 0.721
Find the z value such that P(-z ≤ Z ≤ z) = 0.95. z = -1.645 z = -1.96 z = 1.645 z = 1.96
z = 1.96
