Test 1
. The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time m is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Assume that s remains unchanged at 3 seconds. You decide to test the hypotheses H0: m = 30 versus Ha: m ≠ 30 at the 1% significance level. What is the range of -values for which you will not reject H0? A) (27.424, 32.576) B) (27.674, 32.326) C) (29.141, 30.859) D) (29.225, 30.775)
a
3. A college basketball player is known to make 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 free throws? A) 0.0057 B) 0.2643 C) 0.72 D) 0.90
a
A marketing research firm wishes to determine if the adult men in Laramie, Wyoming, would be interested in a new upscale men's clothing store. From a list of all residential addresses in Laramie, the firm selects a simple random sample of 100 and mails a brief questionnaire to each. What is the population of interest? A) All adult men in Laramie, Wyoming B) All residential addresses in Laramie, Wyoming C) The members of the marketing firm that actually conducted the survey D) The 100 addresses to which the survey was mailed
a
A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let p denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the probability that p will be more than 50% A) Less than 0.0001 B) About 0.1 C) 0.4602 D) 0.50
a
A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions. The number 70.24% is a _________. A) statistic B) parameter C) sample D) population
a
It is claimed that 55% of marriages in the state of California end in divorce within the first 15 years. A large study was started 15 years ago and has been tracking hundreds of marriages in the state of California. Suppose 100 marriages are randomly selected. What is the probability that less than 20 of them ended in a divorce? A) Less than 0.0001 B) 0.0055 C) 0.0130 D) 0.0229
a
Quantitative variables are best displayed using _______. A) stemplots C) bar graphs B) pie charts D) pie charts or bar graphs
a
Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours. An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample. The figure below provides the results of the analysis. Based on the results, the null hypothesis would ______ at the .05 significance level. A) be rejected B) not be rejected
a
Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours. An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample. The figure below provides the results of the analysis. What is the value of the test statistic? A) -2.5 B) 0 C) .006 D) This can't be determined from the given information
a
Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours. An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample. The figure below provides the results of the analysis. 28. The alternative hypothesis is ________. A) one-sided B) two-sided C) three-sided D) four-sided
a
The null hypothesis is a statement about the ________. A) population parameter C) sample mean B) sample statistics D) margin of error
a
The number of Facebook friends students at a university have are Normally distributed with a mean of 1200 and a standard deviation of 200. What percentage of students has at least 1000 Facebook friends? A) 84.13% B) 15.86% C) 42.07% D) None of the above
a
The temperature at any random location in a kiln used for manufacturing bricks is Normally distributed with a mean of 1000°F and a standard deviation of 50°F. If bricks are fired at a temperature above 1125°F, they will crack and must be discarded. If the bricks are placed randomly throughout the kiln, what is the percentage of bricks that crack during the firing process? A) 0.62% B) 2.28% C) 47.72% D) 49.38%
a
To examine the relationship between two variables, the variables must be measured from the same _______. A) cases B) labels C) units D) values
a
Variables that take numeric values for which arithmetic operations make sense are called _______. A) quantitative B) categorical C) distributions D) cases
a
We have a data set where the cases are college students. One of the variables in the data set is "age of the student." What type of variable is age of the student? A) Quantitative C) Quantitative and categorical B) Categorical D) None of the above
a
What is needed to compute a margin of error? A) Sample size, standard deviation, and z* B) Sample mean, sample size, and z* C) Sample median, sample mean, and sample size D) Sample median, sample size, standard deviation, and z*
a
What is needed to compute a sample size, n, to obtain a confidence interval with a specified margin of error, m? A) Standard deviation, m, and z* C) m and z* B) Sample mean, Standard deviation, m, and z* D) Population mean, standard deviation, m, and z*
a
When figure skaters need to find a partner for pair figure skating, it is important to find a partner who is compatible in weight. The weight of figure skaters can be modeled by a Normal distribution. For male skaters, the mean is 170 pounds with a standard deviation of 10 pounds. For female skaters, the mean is 110 pounds with a standard deviation of 5 pounds. Let the random variable X = the weight of female skaters, and the random variable Y = the weight of male skaters. Approximately 90% of the male skaters weigh more than how many pounds? A) 157 pounds B) 163.5 pounds C) 176.5 pounds D) 183 pounds
a
You decide to conduct a survey on your campus. The survey asks, "How do you feel about killing animals for food?" You happen to be wearing a fur coat on the day that you administer the survey. What is the problem with this design? A) Response bias—the respondents already have a general idea on your opinion based on the fur coat. B) Undercoverage—the study should be based on all adults and not just students. C) A poorly worded question—the survey should ask "Killing animals for food is acceptable, right?" D) There are no problems with the study.
a
Ignoring twins and other multiple births, assume babies born at a hospital are independent events with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5. What is the probability that the next three babies are of the same sex? A) 0.125 B) 0.250 C) 0.375 D) 0.500
b
1. Which method will tend to give better statistical results? A) Observational studies B) Experiments C) Neither D) Observational studies and experiments will likely give the same results
b
2. What is the best way to control for lurking variables? A) Compare two or more treatments. B) Randomize to assign experimental units to treatments. C) Repeat each treatment on many units. D) None of the above
b
A baseball enthusiast believes pitchers who strike out a lot of batters also walk a lot of batters. He reached this conclusion by going to the library and examining the records of all major league pitchers between 1990 and 1995. What type of study is his decision based on? A) Anecdotal evidence B) An observational study based on available data C) An observational study based on a sample survey D) An experiment
b
A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be to be considered too large? A) 15 gallons B) 15.31 gallons C) 15.72 gallons D) 16 gallons
b
A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure to ban smoking in all public areas. They select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure. What type of sampling method was used to collect the data? A) A systematic county sample C) A multistage sample B) A stratified sample D) A simple random sample
b
A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their beginning salary is = -2532.7 + 2.12x. Mrs. Kathy Jones started working for the company earning $19,000. She currently earns $40,000. What is the residual for Mrs. Jones? A) $1187.30 C) $2812.70 B) $2252.70 D) Cannot be determined from the information given.
b
A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. What is the probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power? A) 0.01 B) 0.10 C) 0.90 D) 0.99
b
A student organization is trying to decide whether or not to offer more movies on campus. They want to determine whether this idea will appeal to members of both genders. A random sample of 1000 students was asked if they were in favor of more movies on campus. The results by gender are shown in the table below: What proportion of the sampled females is in favor of more movies on campus? A) 0.33 B) 0.5 C) 0.555 D) 0.6
b
A survey was conducted involving 303 subjects concerning their preferences with respect to the size of car they would consider purchasing. The following table shows the count of the responses by gender of the respondents: The data are to be summarized by constructing marginal distributions. In the marginal distribution for car size, the entry for medium cars is ______. A) 0.457 D) 0.508 B) 0.409 E) None of the above
b
Chocolate bars produced by a certain machine are labeled 8.0 ounces. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distribution of x has a standard deviation of 0.01 ounces? A) 10 B) 100 C) 1000 D) This can't be determined unless we know the population follows a Normal distribution.
b
Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually exclusive), then _________. A) P(A and B) = 0.16 B) P(A or B) = 1.0 C) P(A and B) = 1.0 D) P(A or B) = 0.16
b
If you test the effects of different amounts of time (1 hour, 2 hours, and 6 hours) spent watching television per day on the ability to focus better, you are testing time watching television at three different _______. A) treatments B) levels C) factors D) None of the above
b
What is a valid way of selecting a simple random sample of five from a population of size 20? A) Place all the names in a hat and draw five names. B) Use the table of random digits (Table B). C) Use statistical software to select random numbers. D) Only B and C E) All of the above
e
In a statistics class with 136 students, the professor records how much money each student has in their possession during the first class of the semester. The histogram shown below represents the data he collected. What is approximately the number of students with $30 or more in their possession? A) Less than 5 B) About 10 C) About 30 D) More than 100
b
In a study of cars that may be considered classics (all built in the 1970s), the least-squares regression line of mileage (in miles per gallon) on vehicle weight (in thousands of pounds) is calculated to be mileage = 45 - 7.5 × weight The mileage for a small Chevy is predicted to be 22 miles per gallon. What was the weight of this car? A) 172.5 lbs C) 8933 lbs B) 3067 lbs D) Cannot be determined from the information given.
b
In the National Hockey League, a good predictor of the percentage of games won by a team is the number of goals the team allows during the season. Data were gathered for all 30 teams in the NHL and the scatterplot of their Winning Percentage against the number of Goals Allowed in the 2006/2007 season with a fitted least-squares regression line is provided: The least-squares regression line and were calculated to be Winning Percent (%) = 116.95 - 0.26 Goals Allowed = 0.69 For the Winning Percent and Goals Allowed least-squares regression analysis above, which of the following statements is/are TRUE? A) About 69% of the variation in the variable Goals Allowed can be explained by the least-squares regression of Winning Percent on Goals Allowed. B) About 69% of the variation in the variable Winning Percent can be explained by the least-squares regression of Winning Percent on Goals Allowed. C) If the correlation between Winning Percent and Goals Allowed were calculated it would be 0.83. D) A and C are true. E) B and C are true.
b
In the fuel efficiency study of 2007 compact model automobiles, the following histogram of the distribution of the miles-per-gallon fuel efficiency rating in city driving (MPG-City) for automobiles manufactured in Europe was obtained. From the histogram above, showing the distribution of MPG-City, we can see that the A) shape of the distribution is roughly symmetric with one peak. B) distribution is skewed to the left. C) distribution is skewed to the right. D) distribution is roughly symmetric with outlier values to the left. E) shape of the distribution would be easier to see if a stemplot had been constructed instead of the histogram.
b
It has been established that the length of gestation until birth for pregnant women is a random variable that is well modeled by the Normal distribution with a mean of m = 282 days and standard deviation of s = 11 days. Births with gestation time of 258 days or less are considered to be premature births. What is the probability that a randomly selected pregnant woman will give birth to a premature baby? A) 0.2182 D) 0.0183 B) 0.0146 E) Not within ± 0.001 of any of the above C) 0.0018
b
It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snowcovered test track. The tests resulted in a mean stopping distance of x= 212.9 meters. Using the sample results and assuming that stopping distance is a Normally distributed random variable, what is the value of the test statistic? A) 0.05 B) -2.52 C) -9.36 D) -1.04 E) -1.96
b
Large data sets with quantitative variables are best displayed using ________. A) stemplots C) stemplots and histograms B) histograms D) none of the above
b
Probability distributions can be visualized graphically using a _______ for continuous random variables. A) probability histogram C) Q-Q plot B) density curve D) scatterplot
b
Suppose a 99% confidence interval for the mean weight of high school girls (in pounds) is calculated as (102.3, 106.5). If we had measured the weights of each of the girls in kilograms (2.2 pounds = 1 kilogram), then the confidence interval for the mean weight of high school girls in kilograms would have been A) (104.5, 108.7). B) (46.5, 48.4). C) (225.06, 234.3). D) (100.1, 104.3)
b
Suppose we wish to test the hypotheses H0: m = 10 versus Ha: m < 10, where m represents the mean age of children not in high school who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with s = 2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be x= 8.76. What is the value of the P-value? A) 0 B) 0.0066 C) 0.1075 D) 0.2676
b
Suppose you have a perfectly fair 10-sided die, with sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. What are the probabilities of each possible outcome? A) All probabilities are equal to 1/2. B) P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = P(6) = P(7) = P(8) = P(9) = P(10) = 1/10 C) P(1) = P(2) = P(3) = P(4) = P(5) = P(6) = P(6) = P(7) = P(8) = P(9) = P(10) = 1/6 D) None of the above
b
Suppose you own a pizza delivery company and you are trying to determine the best campus on which to sell pizza. What would be the best measurement to make the comparison? A) Average number of pizzas purchased C) Rate of pizzas purchased B) Count of pizzas purchased D) None of the above
b
The Michigan Department of Transportation (M-DOT) is working on a major project: 80% of the highways in Michigan need to be repaved. To speed completion of this project, many contractors will be working for M-DOT. Contractors are currently bidding on the next part of the project. To help make a decision about which contractor to hire, M-DOT collects many variables besides just the estimated cost. One of those variables is the contractor's estimate of the number of workdays required to finish the job. Twenty contractors have bid on the next job. The boxplot below represents their estimates of the number of work days required. What is (approximately) the interquartile range, based on the boxplot? A) 140 days B) 270 days C) 360 days D) 760 days
b
The least-squares regression line always passes through the point ____. A) (0,0) C) (median of x, median of y) B) x, y D) None of the above
b
Thousands of batteries are produced every day in a certain manufacturing plant. The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance, like a portable radio or CD player. The quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days. These batteries will be put into a variety of moderately sized appliances and the average of all failure times will be computed. Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries? A) The uniform distribution C) The binomial distribution B) The Normal distribution D) The Weibull distribution
b
When trying to explain the relationship between two quantitative variables, it would be best to use a _______. A) density curve B) scatterplot C) boxplot D) histogram
b
Which of the following define a complete and valid probability model? A) S = {A, B, C}; P(A) = 1/3, P(B) = 2/3, P(C) = 1 B) S = {H, T}; P(H) = 1/4, P(T) = 3/4 C) S = {W, X, Y, Z}; P(W) = 1/4, P(X) = 1/4, P(Z) = 1/4 D) P(RED) = 1/2, P(BLUE) = 1/2
b
Which of the following statements about a scatterplot is/are TRUE? A) It is always necessary to identify one of the two variables as the explanatory variable and the other as the response variable. B) On a scatterplot we look for overall patterns showing the form, direction, and the shape of the relationship. C) Because a scatterplot requires the values of two quantitative variables, it is never possible to add one or more categorical variables to the graph. D) Both A and B are true statements. E) None of the above statements are true
b
1. A particularly common question in the study of wildlife behavior involves observing contests between "residents" of a particular area and "intruders." In each contest, the residents either win or lose the encounter (assuming there are no ties). Observers might record several variables, some of which are listed below. Which of these variables is categorical? A) The duration of the contest (in seconds) C) Whether the residents win or lose B) The number of animals involved in the contest D) The total number of contests won by the residents
c
A distributor of electronics is doing a customer satisfaction survey for a manufacturer of tablet computers. A sample of 68 clients is asked to rate a particular tablet on appearance, functionality, ease of use, and price on a scale of 1 to 10, where 1 corresponds to the worst rating and 10 to the best possible rating. A bar graph of the ease of use ratings classified by gender is given below. What percentage of the sampled female clients rated the tablet as not so easy to use (a rating of 4 or lower)? A) 28% B) 29% C) 38% D) 62%
c
A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. What proportion of tanks will hold between 14.75 and 15.10 gallons of gas? A) 0.35 B) 0.6563 C) 0.6997 D) 0.9833
c
A population variable has a distribution with a mean of m = 50 and a variance of s2 = 225. From this population a simple random sample of n observations is to be selected and the mean of the sample values calculated. How big must the sample size n be so that the standard deviation of the sample mean is equal to 1.4 (i.e., = 1.4)? A) n = 11 B) n = 161 C) n = 115 D) n = 36 E) n = 21
c
A small store keeps track of X = the number of customers who make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. Suppose the store is open 7 days per week from 8:00 a.m. to 5:30 p.m. What is the mean number of customers who make a purchase during the first hour that the store is open during a 1-week period? A) 3.0 B) 9.0 C) 21.0 D) 28.0
c
A student organization is trying to decide whether or not to offer more movies on campus. They want to determine whether this idea will appeal to members of both genders. A random sample of 1000 students was asked if they were in favor of more movies on campus. The results by gender are shown in the table below: What proportion of the sampled students is in favor of more movies on campus? A) 0.33 B) 0.5 C) 0.555 D) 0.6
c
A survey was conducted involving 303 subjects concerning their preferences with respect to the size of car they would consider purchasing. The following table shows the count of the responses by gender of the respondents: In the conditional distribution for preference of car size among male respondents, the entry for large cars is _______. A) 0.056 D) 0.139 B) 0.405 E) None of the above C)0.152
c
At the end of a production run manufacturing rubber gaskets, items are sampled at random and inspected to determine if the item is acceptable (A) or defective (D). Suppose it is planned to select two items and determine if each is either A or D. What is the sample space S of the outcomes? A) S = {A or D} B) S = {AA, DD} C) S = {AA, AD, DA, DD} D) This depends upon the assignment of probability to the outcomes of the sampling. E) This can't be determined until the sample of two items has been collected.
c
Consider any two events A and B, such that P(A) ≠ 0 and P(B) ≠ 0. Which of the following statements is always FALSE? A) If events A and B are independent, then P(A|B) = P(A) and P(B|A) = P(B). B) If events A and B are disjoint, then P(A and B) = 0. C) If events A and B are independent, then P(A and B) = 0. D) If events A and B are disjoint, then they are not independent. E) If events A and B are independent, then P(A and B) = P(A)P(B).
c
During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below are separate stemplots for the number of home runs by American League and National League teams based on the team-by-team statistics on home runs hit through Friday, June 3, 1994 (from the Columbus Dispatch, Sunday, June 5, 1994). Legend: 2|9 represents 29. What is the mean for the number of home runs for the National League teams? A) 45 B) 50 C) 50.1 D) 57.5
c
In a study of 1991 model cars, a researcher computed the least-squares regression line of price (in dollars) on horsepower. He obtained the following equation for this line. price = -6677 + 175 × horsepower Based on the least-squares regression line, what would we predict the cost to be of a 1991 model car with horsepower equal to 200? A) $41,677 B) $35,000 C) $28,323 D) $13,354
c
On a chilly spring afternoon, 10 lab sections of a statistics class all have full attendance. The 10 lab sections each have the same number of students enrolled in it. A class evaluation is about to be administered to some of the students. It has been decided to first randomly select 3 of the 10 lab sections and then give the evaluation to a simple random sample of one-fourth of the students in those sections. What sampling technique is being used? A) Simple random sampling C) Multistage sampling B) Stratified random sampling D) Convenience sampling
c
One hundred volunteers who suffer from severe depression are available for a study. Fifty are selected at random and are given a new drug that is thought to be particularly effective in treating severe depression. The other 50 are given an existing drug for treating severe depression. A psychiatrist evaluates the symptoms of all volunteers after 4 weeks in order to determine if there has been substantial improvement in the severity of the depression. In which situation would this study be double blind? A) If neither drug had any identifying marks on it B) If all volunteers were not allowed to see the psychiatrist nor was the psychiatrist allowed to see the volunteers during the session when the psychiatrist evaluated the severity of the depression C) If neither the volunteers nor the psychiatrist knew which treatment any person had received D) All of the above
c
Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Normal distribution with standard deviation s = 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for m is found to be 512.00 ± 25.76." What was the confidence level used to calculate this confidence interval? A) 90% B) 95% C) 99% D) 99.9%
c
Suppose that the random variable X is continuous and takes its values uniformly over the interval from 0 to 2. What is the value of the probability P{X ≤ 0.4 or X > 1.2}? A) 0.40 B) 0.20 C) 0.60 D) 0.80 E) 0.50
c
Suppose we roll a red die and a green die. Let R be the event that the number of spots showing on the red die is three or less, and G be the event that the number of spots showing on the green die is more than three. The events R and G are _________. A) disjoint B) complements C) independent D) reciprocals
c
Suppose you are going to roll a six-sided die 60 times and record , the proportion of times that an even number (2, 4, or 6) is showing. Suppose you decide to roll the die 200 times instead of 60 times. How will this affect the center and spread of the sampling distribution of ? A) Both the center and the spread will remain the same. B) The center will remain the same, but the spread will increase. C) The center will remain the same, but the spread will decrease. D) Both the center and the spread will decrease.
c
The British government conducts regular surveys of household spending. The average weekly household spending on tobacco products and spending on alcoholic beverages for each of 11 regions in Great Britain were recorded. A scatterplot of spending on tobacco versus spending on alcohol is given below:What is the most plausible value for the correlation between spending on tobacco and spending on alcohol? A) 0.99 B) 0.8 C) 0.08 D) -0.8
c
The World Malaria Report (2008) has information on the number of reported malaria cases from 2005 and 2006 for the 10 countries listed in West Africa. The data are presented in the table below. If the number of reported malaria cases in Sierra Leone were mistyped and reported as 1,160,666, what would happen to the mean and median? A) Both would remain unchanged. B) The mean would change, but the median would stay the same. C) The mean and median would change. D) You cannot tell without doing the actual calculation.
c
The heights of young American women, in inches, are Normally distributed with a mean of m and a standard deviation of s = 2.4. A simple random sample of four young American women is selected and their heights measured. The four heights, in inches, are 63, 69, 62 and 66. Based on these data, what is a 99% confidence interval for m? A) 65.00 ± 1.55 B) 65.00 ± 2.35 C) 65.00 ± 3.09 D) 65.00 ± 4.07
c
The lack of a linear relationship between two quantitative variables is represented by the correlation, r, with values ________. A) greater than zero B) less than zero C) equal to zero D) equal to 1 or -1.
c
The scores of individual students on the American College Testing (ACT), a college readiness assessment, have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the sampling distribution of the sample mean score for a random sample of 36 students? A) Approximately Normal, but the approximation is poor B) Approximately Normal, and the approximation is good C) Exactly Normal D) Neither Normal nor non-Normal—it depends on the particular 36 students selected
c
The table below shows the political affiliations of 1000 randomly selected American voters and their positions on the school of choice program.Let the event D = {voter is a Democrat}, R = {voter is a Republican}, and F = {voter favors the school of choice program}. For each of the following questions, write the probability in symbols (e.g., P(D)) and calculate the probability. 32. What is the probability that a randomly selected Republican favors the school of choice program? A) P(F|R) = 0.12 B) P(R|F) = 0.19 C) P(F|R) = 0.33 D) P(R|F) = 0.36
c
The table below shows the political affiliations of 1000 randomly selected American voters and their positions on the school of choice program.Let the event D = {voter is a Democrat}, R = {voter is a Republican}, and F = {voter favors the school of choice program}. For each of the following questions, write the probability in symbols (e.g., P(D)) and calculate the probability.A candidate thinks she has a good chance of gaining the votes of anyone who is a Democrat or who is in favor of the school of choice program. What proportion of the 1000 voters is that? A) P(D or F) = 0.26 B) P(D and F) = 0.65 C) P(D or F) = 0.66 D) P(D|F) = 0.92
c
The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random variable with a mean of m = 10 ounces and a standard deviation of s = 1 ounces. Suppose we pick four tomatoes from the bin at random and put them in a bag. Define the random variable Y = the weight of the bag containing the four tomatoes. What is the standard deviation of the random variable Y? A) s Y = 0.50 ounces B) s Y = 1.0 ounces C) s Y = 2.0 ounces D) s Y = 4.0 ounces
c
When constructing confidence intervals, the center of each interval is always _______. A) the median B) the margin of error C)x D) the mode
c
. A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the mean, , of the sampling distribution of ? A) 5% B) 6% C) 40% ± 5% D) 0.40
d
. A test of significance was conducted in a study involving a random sample of 25 subjects. Based on the test result using the sample mean , it was determined that the P-value was equal to 0.028. Which of the following statements about this P-value is/are TRUE? A) In this situation there is relatively strong evidence against the null hypothesis. B) The P-value was calculated under the assumption that the null hypothesis was true. C) The probability of a value of the test statistic at least as extreme as that observed in this study, assuming the null hypothesis is true, is 0.028. D) All of the above are true statements.
d
. In tests of significance about an unknown parameter, what does the test statistic represent? A) The value of the unknown parameter under the null hypothesis B) The value of the unknown parameter under the alternative hypothesis C) A measure of compatibility between the null and alternative hypotheses D) A measure of compatibility between the null hypothesis and the data
d
A sample of size n is selected at random from a population that has mean m and standard deviation s. The sample mean will be determined from the observations in the sample. Which of the following statements about x the sample mean x is/are TRUE? A) The mean x of is the same as the population mean (i.e., m). B) The variance of x is o^2/n. C) The standard deviation of x decreases as the sample size grows larger. D) All of the above are true. E) Only A and B are true
d
A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision. Based on an examination by a qualified professional, the individuals were judged as to whether or not they needed to wear glasses for reading. In addition it was determined whether or not they were currently using glasses for reading. The following table provides the proportions found in the study. If a single adult is selected at random from this large population, what is the probability that the adult is judged to need eyeglasses for reading? A) 0.46 B) 0.42 C) 0.78 D) 0.60 E) 0.40
d
A television station is interested in predicting whether or not voters in its listening area are in favor of federal funding for abortions. It asks its viewers to phone in and indicate whether they are in favor of or opposed to this. Of the 2241 viewers who phoned in, 1574 (70.24%) were opposed to federal funding for abortions. What type of sampling method was used to collect the data? A) A simple random sample B) A stratified random sample C) A probability sample in which each person in the population has the same chance of being in the sample D) Voluntary response
d
Below is a data set with information on students in a basic statistics class at a local university. What is a key characteristic of the data set? A) There are 10 students in the data set. C) There are three variables in the data set. B) The data describe students in a class. D) All of the above
d
Consider the following probability histogram for a discrete random variable X. What is P(X ≤ 3)? A) 0.10 B) 0.25 C) 0.35 D) 0.65
d
It is estimated that chemotherapy is successful 70% of the time in curing a particular type of cancer. Suppose that four patients with the given type of cancer are treated, and let X be the number of them that are successfully cured. What is the expected value of the number of patients that will be cured? A) 3 B) 2 C) 0.2 D) 2.78 E) 2.5
d
It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snowcovered test track. The tests resulted in a mean stopping distance of x= 212.9 meters. What is the P-value? A) 0.012 D) 0.006 B) 0.050 E) Not within ± 0.002 of any of the above C) 0.025
d
Seventy-five college students took part in a study initiated by a large computer manufacturer. The company is designing a new type of laptop computer and has created prototypes of it with two different keyboard designs. They are also including the current design of the laptop in the experiment. Each of the students was randomly assigned to one of the three types of computers. The students were asked to spend 15 minutes on one of the computers, performing several tasks (typing words, numbers, making corrections, etc.). The ease of use of the keyboard was then rated on a five-point scale by having the students fill out a short questionnaire. Which of the following basic principles of statistical design was not used in this experiment? A) Control B) Randomization C) Repetition D) Blinding
d
Suppose a simple random sample is selected from a population with a mean if m and a variance of s2. The central limit theorem tells us that A) the sample mean gets closer to the population mean m as the sample size increases. B) if the sample size n is sufficiently large, the sample will be approximately Normal. C) the mean of x will be m if the sample size n is sufficiently large. D) if the sample size is sufficiently large, the distribution of will be approximately Normal with a mean of m and a standard deviation of o/ √n . E) the distribution x of will be Normal only if the population from which the sample is selected is also Normal.
d
Suppose we have two independent random variables X and Y. Which of the following statements about X and Y is FALSE? A) The mean of X + Y is the sum of their means. B) The variance of X + Y is the sum of their variances. C) The correlation between X and Y is zero. D) The variance of the difference of X - Y is the difference of their variances. E) The mean of the difference of X - Y is the difference of their means.
d
The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with s = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of x= 1038. Construct a 92% confidence interval estimate for the mean lifetime m. If it were desired to cut the confidence interval to half its length while keeping the same 92% level, what size sample would be required to achieve this? A) 50 B) 13 C) 75 D) 100 E) 41
d
The preparation time to mail envelopes with a weekly report to all executives in a company has a Normal distribution with a mean of 35 minutes and a standard deviation of 2 minutes. On 95% of such occasions, the mailing preparation takes less than x minutes. What is the value of x? A) 31.71 B) 34.75 C) 35.25 D) 38.29
d
The variable Z has a standard Normal distribution. Find the value z such that 85% of the observations fall below z. A) z = -1.04 B) z = 0.80 C) z = 0.85 D) z = 1.04
d
Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z < 1.1? A) 0.1357 B) 0.2704 C) 0.8413 D) 0.8643
d
Which of the following are independent trials? A) The results of a coin flip after rolling two dice B) The first character of a license plate and the color of the car C) The total of two dice after recording the value of the first die rolled D) A and B E) All of the above
d
4. A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. If a sample of 100 individuals, 12 years of age or older, were selected at random from the Canadian population, we could use the Normal distribution to approximate the probability that more than 38 of the sampled people had their most recent eye examination in the previous year because A) the population is very much larger than the sample size. B) np > 10, and n(1 - p) > 10. C) independence can be assumed, since the people were selected at random. D) the probability of the eye examination can be assumed to be constant from person to person in the sample. E) All of the above
e
In the National Hockey League, a good predictor of the percentage of games won by a team is the number of goals the team allows during the season. Data were gathered for all 30 teams in the NHL and the scatterplot of their Winning Percentage against the number of Goals Allowed in the 2006/2007 season with a fitted least-squares regression line is provided: The least-squares regression line and were calculated to be Winning Percent (%) = 116.95 - 0.26 Goals Allowed = 0.69 Which of the following provides the best interpretation of the slope of the regression line? A) If the Winning Percent increases by 1%, then the number of Goals Allowed decreases by 0.26. B) If a team were to allow 100 goals during the season, their Winning Percent would be 90.95%. C) If Goals Allowed increases by one goal, the Winning Percent increases by 0.26%. D) If the Winning Percent increases by 1%, then the number of Goals Allowed increases by 0.26. E) If Goals Allowed increases by one goal, the Winning Percent decreases by 0.26%.
e
