exam 3 questions
There is a strong straight-line association between the height and the arm lengths of a group of people. Knowing this, a reasonable value for the correlation coefficient between height and arm length is: a. 0.8 b. 0.2 c. -0.2 d. -0.8
a
The psychologist Amos Tversky did various studies of our perception of chance behavior. Tversky asked subjects to choose between two public health programs that affect 600 people. The first program has probability 1/2 of saving all 600 and probability 1/2 that all 600 will die. The expected number of people saved by the first program is ___. a. 600 people b. 0 people c. 300 people d. 0.5 people
c
Tonya wants to estimate the proportion of the students in her dormitory who like the dorm food. She interviews an SRS of 50 of the 500 students living in the dormitory. She finds that 14 students think that the dorm food is good. Identify the population proportion p. a. The proportion of all residents of the dorm who were interviewed by Tonya. b. The proportion of all students in the SRS who like the food. c. The proportion of all residents of the dorm who like the food.
c
You want to estimate the probability that the player makes seven or more of 10 shots. You simulate 10 shots 25 times and get the following numbers of hits: 7, 9, 7, 6, 3, 7, 5, 6, 5, 6, 7, 5, 6, 6, 8, 5, 6, 3, 9, 6, 7, 7, 8, 7, 9 What is your estimate of the probability? a. 15/25 or 0.20 b. 11/25, or 0.44 c. 12/25, or 0.48 d. 13/25, or 0.52 e. 14/25, or 0.56
c
A 95% confidence interval for the true mean resting heart rate for those who exercise is 62.87 < µ < 69.13 beats per minute (bpm). Choose the correct interpretation of this interval. a. We are 95% sure that the true mean blood pressure for those who exercise is no less than 62.87 and no more than 69.13 bpm. b. We are 95% confident the sample mean blood pressure for those who exercise is no less than 62.87 and no more than 69.13 bpm. c. We are 95% confident the true mean blood pressure for those who exercise is no less than 62.87 and no more than 69.13. d. We are 95% confident the true mean blood pressure for those who exercise is no less than 62.87 and no more than 69.13 bpm.
d
If the correlation coefficient r = 0.5 then the coefficient of determination (or r squared) is a. 0.10 b. 0.25 c. 0.71 d. 1.00 e. 2.50
b
If there were something genetic which made people simultaneously more susceptible to both smoking and lung cancer, that would be an instance of a. causation b. common response c. confounding
b
There is a strong straight-line relationship between the outdoor temperature and the amount of energy used to heat a house. Lower temperatures require more energy to keep the house warm. Knowing this, a reasonable value for the correlation coefficient between temperature and home energy consumption is: a. 0.9 b. 0.3 c. -0.3 d. -0.9
d
A baseball player makes 30% of his at-bats during the season. Use 00 to 29 as a hit and 30 to 99 are a miss. Using that information, use these random digits to simulate 10 at-bats: 82234 71490 20467 47511 81676 55300 94383 14893 How many of these 10 at-bats are hits? 4, 10, 5, 3
4
You choose an SRS of 2000 women over 18 years of age from the New York City metropolitan area; 623 of them are single. A 90% confidence interval for the proportion of all adult women in the New York area who are single is a. 0.31 ± 0.017 b. 0.31 ± 0.026 c. 0.62 ± 0.017 d. 0.62 ± 0.026
a
Which of the following statements is true of a 95% confidence interval? a. 95% of all possible 95% confidence intervals form this population will contain the true parameter. b. The margin of error for the statistic is 95%. c. The standard deviation of the statistic is 0.95. d. The statistic is within 5% of the parameter.
a
A grocery chain runs a prize game by giving each customer a ticket that may win a prize when a box is scratched. Printed on the ticket are the following probabilities for a customer who shops once a week: Amount won Probability $1000 0.01 $100 0.10 $10 0.20 $0 0.69 What is the expected value of a customer's winnings in this game? a. $22 b. $10 c. $100 d. $.31
a
A random number generator comes from a population with µ = 0.5. A commend to generate 100 random number gives outcomes with means (x-bar) = 0.536 and s = 0.312. Give a 90% confidence interval for the mean of all numbers produced by the software. a. 0.474 to 0.598 b. 0.505 to 0.567 c. 0.485 to 0.587 d. 0.467 to 0.605
c
You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. To simulate an outcome with probability 0.11, you could a. look at two digits in the random number table; the outcome occurs if the digits are 11. b. look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ..., 11. c. look at two digits in the random number table; the outcome occurs if the digits are any of 00, 01, ..., 10. d. look at two digits in the random number table; the outcome occurs if the digits are any of 01, 02, ..., 11. e. Both (C) and (D) are correct simulations.
e
Which of the following values could not represent a correlation coefficient? a. r = 0.99 b. r = 1.09 c. r = -0.73 d. r = -1.0
b
the pattern of values a statistic can take when sampling repeatedly from a population is a. bias of the statistic b. sampling variability of the statistic c. sampling distribution of the statistic d. standard error of the statistic
c
There is a close relationship between the correlation r and the slope b of the least-squares regression line. In particular, it is true that a. r and b always have the same sign, which shows whether the variables are positively or negatively associated b. r and b both always take values between - 1 and 1. c. the slope b is always at least as large as the correlation r d. the slope b is always equal to r2, the square of the correlation
a
Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in a statistics class is r = 0.85 . One interpretation r is to say what percent of the variation in Exam 2 scores can be explained by the straight line relationship between Exam 2 scores and Exam 1 scores. This percent is about a. 85% b. 72% c. 49% d. 30%
b
If the distribution of cricket singing times is skewed right, the distribution for the sample mean of 30 observations from this distribution will be a. skewed right b. skewed left c. symmetric d. cannot be determined
c
A basketball player makes 65% of her shots from the field during the season. To simulate whether a shot hits or misses which one of the following would be an appropriate assignment of digits: a. One digit simulates one shot; 6 and 5 are a hit, other digits are a miss. b. One digit simulates one shot; odd digits are a hit and even digits are a miss. c. Two digits simulate one shot; 01 to 65 are a hit and 66 to 99 are a miss. d. Two digits simulate one shot; 01 to 65 are a hit and 66 to 99 and 00 are a miss.
d
Referring to a hypothesis test, identify the correct interpretation of a P-value of 0.02 a. There is a 1 in 50 chance of not seeing this much evidence against HO when it is false b. There is a 1 in 50 chance of seeing this much evidence against HO when it is false c. There is a 1 in 50 chance of not seeing this much evidence against HO when it is true d. There is a 1 in 50 chance of seeing this much evidence against HO when it is true
d
Suppose we have the following distribution of outcomes for a "loaded" die. Probability 0.5 0.1 0.1 0.1 0.1 0.1 Outcome 1 2 3 4 5 6 Find the expected number you'll get when rolling this die. A.1 B. 1.5 C. 2 D. 2.5 E. 3
d
Here is a two-way table of the responses of a sample of 500 teenage girls and 500 teenage boys to the question "Is it always wrong to have sex before marriage?" Boys Girls Yes 205 275 No 220 Not sure 10 5 The missing table entry should be a. 205 b. 275 c. 280 d. 285 Using the two-way table in the above problem, find the critical value at 95% confidence using Table 24.1 in book. a. 5.99 b. 7.81 c. 9.49 d. 11.07
d, a
Tonya wants to estimate the proportion of the students in her dormitory who like the dorm food. She interviews a SRS of 50 of the 500 students living in the dormitory. She finds that 14 students think that the dorm food is good. Find the sample proportion (p-hat) of those that like dorm food. a. 14 b. 14/50 = 0.28 c. 14/500= 0.028 d. 50/500= 0.10
b
You find the 95% confidence interval of voters who agree with the president's health reform to be 0.6 ± 0.03 . A 90% confidence interval based on the same sample size as the above 95% confidence interval would have a. the same center and a larger margin of error b. the same center and a smaller margin of error c. a larger margin of error and probably a different center d. a smaller margin of error and probably a different center
b
You read that "the correlation between a person's sex and his or her occupation is r=0.32." This statement is improper because a. 0.32 is not a possible value for a correlation. b. correlation can't be used to describe association between two categorical variables. c. the association is negative, so the correlation must be less than zero. d. the five-number summary is a better description of these data.
b
A study of drug addicts in Amsterdam recorded how often each addict had recently injected drugs and whether or not the addict was infected with HIV, the virus that causes AIDS. Here is a two-way table of the numbers of addicts in each condition: HIV Yes HIV No Daily 32 45 Inject> Less than daily 20 18 No 18 23 About what percent of addicts who inject daily are infected with HIV? a. 20.5% b. 41.6% c. 44.9% d. 45.7% Using above two-way table, what is the table total? a. 77 b. 86 c. 156 d. 312
b, c
If a significance test gives a P-value 0.005, a. the margin of error is 0.005 . b. the null hypothesis is very likely to be true. c. we do not have good evidence against the null hypothesis. d. we do have good evidence against the null hypothesis.
d
The correlation between two variables x and y is -0.6. If we used a regression line to predict y using x, what percent of the variation in y would be explained? a. -36% b. 6% c. 20% d. 36%
d
Using the information in the above problem, on a day when the temperature is 20 degrees F, the regression line predicts that gas used will be about a. 1724 cubic feet b. 1383 cubic feet c. 1325 cubic feet d. 964 cubic feet
d
A study of fathers' involvement in their children's education interviews a sample of fathers of school-age children. One question concerns regularly scheduled parent-teacher conferences. Here is a two-way table of the results: Attended Attended Attended all some none Fathers in two-parent families 109 132 203 Fathers in single-parent families 15 10 13 Non-resident fathers 31 45 82 Using the two-way table, find the critical value with 95% confidence for this problem using Table 24.1 in book (also shown in lecture notes). a. 5.99 b. 7.81 c. 9.49 d. 11.07 What is the expected value for fathers in single-parent families who attend all parent-teacher conferences. a. 3.63 b. 9.20 c. 15.0 d. 38.27 The observed counts in the father's involvement table are given above. Let's say you calculate the expected count of non-resident fathers who attend no parent-teacher conferences to be 73.57 . What the Chi-square statistic term for that one cell? a. .11 b. .97 c. 1.12 d. 8.43 The Chi-Square statistic for this two-way table is 7.51. We can conclude that a. There is very strong evidence that family status and fathers' attendance at school conferences are related in the population of all fathers. Therefore, one could say that father's attendance at school conferences is dependent on family status. b. There is very strong evidence that family status and fathers' attendance at school conferences are related among the fathers in this sample. Therefore, one could say that father's attendance at school conferences is dependent on family status but only for this sample of fathers. c. We lack strong evidence that family status and fathers' attendance at school conferences are related in the population of all fathers. Therefore, one could say that father's attendance at school conferences is independent of family status. d. We lack strong evidence that family status and fathers' attendance at school conferences are related among the fathers in this sample. Therefore, one could say that father's attendance at school conferences is independent of family status but only for this sample of fathers.
c, b, b, c
Larry Bird made 90% of his free throws. To simulate one free throw shot by Larry Bird, we could use a random digit with a. odd = made, even = missed. b. 0 to 8 = made, 9 = missed. c. 0 to 4 = made, 5 to 9 = missed. d. 1 to 9 = made, 0 = missed. e. Either (A) or (C) is correct. f. Either (B) or (D) is correct.
f
Suppose we take a SRS which results in p-hat = 0.35 and estimated standard deviation of p-hat = 0.05. Find a 95% confidence interval for p. a. 0.3 < p < 0.4 b. 0.25 < p < 0.45 c. 0.05 < p < 0.65 d. 0 < p < 0.79
b
You would draw a scatterplot a. to show the distribution of heights of students in this course. b. to show the relationship between heights of female students and heights of their mothers. c. to show a child's height over time. d. to compare the distributions of heights for male and females students in this course.
b
You gather data on the number of hours of television news broadcasts watched per week and the grade point average of juniors majoring in journalism. You expect that TV news broadcast watching will help explain grades. In a scatterplot of your data, a. hours of TV new broadcast watching should be on the x-axis. b. grade index should be on the x-axis. c. it makes no difference which is horizontal. d. a scatterplot is not an appropriate type of graph for these data.
a
Here is a two-way table of the numbers of college students (U.S. citizens only) classified by racial/ethnic group and by whether they attend a public or a private college. The entries are in thousands of students. Public Private Non-Hispanic White 7094 1982 Non-Hispanic Black 831 290 Hispanic 336 47 Asian 166 32 Native American 68 9 What percent of public college students are non-Hispanic blacks? a. 9.8% b. 10.4% c. 13.3% d. 26.6% Using the table above, find the expected count for Asians who attend public school. Answers: a 43.05 b. 60.26 c. 154.95 d. 166.0 Using the two-way table in the above problem, find the critical value at 95% confidence using Table 24.1 in book. a. 5.99 b. 7.81 c. 9.49 d. 11.07
a, c, c
A grocery chain runs a prize game by giving each customer a ticket that may win a prize when a box is scratched. Printed on the ticket are the following probabilities for a customer who shops once a week: Amount won Probability $1000 0.01 $100 0.10 $10 0.20 $0 0.69 If several thousand customers play the grocery store game, you expect that the mean amount they win will be close to a. the probability of winning something b. the median amount they win c. the expected value of a customer's winnings d. $100.00
c
An agricultural economist says that the correlation between corn prices and soybean prices is r=0.7. This means that a. when corn prices are above average, soybean prices also tend to be above average. b. there is almost no relation between corn and soybean prices. c. when corn prices are above average, soybean prices tend to be below average. d. the economist is confused because correlation makes no sense in this situation.
a
Choose an American household at random and ask how many computers that household owns. Here are the probabilities as of 2003: Number of computer 0 1 2 Probability 0.38 0.44 0.18 What is the expected number of computers a household owns? a. 0.80 b. 1 c. 1.18 d. 1.44
a
In a standard deck of 52 cards, there are 13 spades, 13 hearts, 13 diamonds, and 13 clubs. Identify the correct assignment of digits for a simulation to determine the suit (spades, hearts, diamonds, or clubs) of a card chosen at random from a standard deck of 52 cards? a. 01, 02, 03, ..., 25 = spades 26, 27, 28, ..., 50 = hearts 51, 52, 53, ..., 75 = diamonds 76, 77, 78, ..., 99, 00 = clubs b. 01, 02, 03, ..., 25 = spades 26, 27, 28, ..., 50 = hearts 51, 52, 53, ..., 75 = diamonds 76, 77, 78, ..., 99 = clubs c. 1, 2, 3, ..., 13 = spades 14, 15, 16, ..., 26 = hearts 27, 28, 29, ..., 39 = diamonds 40, 41, 42, ..., 52 = clubs d. 1, 2, 3 = spades 4, 5, 6 = hearts 7, 8 = diamonds 9, 0 = club
a
Referring to a hypothesis test, identify the correct interpretation of the significance level (α- level) of the test a. The percent of time you're willing to reject HO when HO is true b. The percent of time you're willing to reject HA when HA is true c. The percent of time you're willing to fail to reject HO when HO is true d. The percent of time you're willing to fail to reject HA when HA is true
a
The question was asked "Do you think what is shown on television today is less moral than American society, more moral, or accurately reflects morality in American society?" Of the answers, 46% said "Less", 37% said "Accurate", 9% said "More", and 8% had no opinion. We might use these data to answer the question, "Do more than half of all adults think TV is less moral than society?" To do this, our null hypothesis would be a. p = 0.5 b. p < 0.5 c. p > 0.5 d. p ≠ 0.5
a
Tonya wants to estimate the proportion of the students in her dormitory who like the dorm food. She interviews an SRS of 50 of the 500 students living in the dormitory. She finds that 14 students think that the dorm food is good. Identify the population which Tonya wants to draw conclusions about. a. The 500 students who live in the dormitory. b. The 50 students who live in the dormitory. c. The 450 students who are not interviewed by Tonya.
a
Use 00-74 to simulate passing a class and 75-99 to simulate failing a class for a college student. Use the following list of random digits to simulate 5 classes and select the correct result of this simulation 29564 46790 33291 14632 a. 4 passed b. 5 passed c. 7 passed d. 9 passed
a
Which of the following statement about correlation is false? a. The correlation coefficient cannot be 0. b. The correlation coefficient can never be larger than 1. c. The correlation coefficient measures how tightly the points in a scatterplot cluster about a straight line.
a
The question was asked "Do you think what is shown on television today is less moral than American society, more moral, or accurately reflects morality in American society?" Of the answers, 46% said "Less", 37% said "Accurate", 9% said "More", and 8% had no opinion. We might use these data to answer the question, "Do more than half of all adults think TV is less moral than society?" To do this, our alternative hypothesis would be a. p = 0.5 b. p < 0.5 c. p > 0.5 d. p ≠ 0.5
b
The student newspaper at a college asks an SRS of of 250 undergraduates, "Do you favor eliminating the carnival from the term-end celebration?" In all, 150 of the 250 are in favor. The 80% confidence interval would be a. (0.57,0.63) b. (0.56,0.64) c. (0.54,0.66) d. (0.52,0.68)
b
How well does the number of beers a student drinks predict his or her blood alcohol content? Sixteen student volunteers at Ohio State University drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC). A scatterplot of the data appears below. The least-squares regression line for predicting blood alcohol content from number of beers is y = -0.013 + 0.018 x . The slope 0.018 of this line tells us that a. the correlation between number of beers and BAC is 0.018. b. on average, BAC increases by 0.018 for each additional beer a student drinks. c. a student who drinks no beer will still have a BAC of 0.018 d. the average BAC of all the students in the study was 0.018 Using the information, the scatterplot shows a. a weak negative straight line relationship b. almost no linear relationship c. a moderately positive straight line relationship d. a perfect positive straight line relationship you predict that the BAC of a student who drinks 15 beers will be about a. 0.203 b. 0.216 c. 0.257 d. Cannot be predicted. a student who drinks no beer will still have a BAC of a. - 0.018 b. 0.018 c. -0.013 d. 0.013
b, c, d, c
A recent Gallup Poll interviewed a random sample of 1523 adults. Of these, 868 bought a lottery ticket in the past year. Suppose that in fact (unknown to Gallup) exactly 60% of all adults bought a lottery ticket in the past year. If Gallup took many SRSs of 1523 people, the sample proportion who bought a ticket would vary from sample to sample. The sampling distribution would be close to normal with a. mean of 0.57 and standard deviation of 0.0126 b. mean of 0.57 and standard deviation of 0.00016 c. mean of 0.6 and standard deviation of 0.0126 d. mean of 0.6 and standard deviation of 0.00016
c
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line for predicting y from x is gas consumption = 1344 - 19 (temperature). When the temperature goes up 1 degree, what happens to the gas usage predicted by the regression line? a. It goes up 1 cubic foot . b. It goes down 1 cubic foot. c. It goes down 19 cubic feet. d. It goes up 19 cubic feet.
c
An October 2004 Gallup Poll asked a sample of 1012 adults whether they thought that having a gun in the house makes it a safer place to be or a more dangerous place to be. The number who thought having a gun in the house makes it a safer place was 425. Although the samples in national polls are not SRSs, they are similar enough to the method that gives approximately correct confidence intervals. Fill in the blanks: The 95 percent confidence interval for the population proportion p is from ___ to ___. (Give your answers to four decimal places.) a. 0.4195 < p < 0.4205 b. 0.4045 < p < 0.4355 c. 0.3896 < p < 0.4504
c
The question was asked "Do you think what is shown on television today is less moral than American society, more moral, or accurately reflects morality in American society?" Of the answers, 46% said "Less", 37% said "Accurate", 9% said "More", and 8% had no opinion. The P-value for the test in the above problem is about 0.99 . The means that a. the poll gives very strong evidence that more than half of adults feel TV is less moral than society. b. the poll gives weak evidence that more than half of adults feel TV is less moral than society. c. the polls sheds no light on whether more than half of adults feel TV is less moral than society. d. the polls gives no evidence that more than half of adults feel TV is less moral than society.
d
There is a 22% probability of rain tomorrow, a 10% chance of just being cloudy, and a 68% chance of being sunny. To simulate the weather for tomorrow we could assign digits in the following way: a. One digit simulates the weather; 1,2 for rain 3 for cloudy, and 4,5,6 for sunny b. Two digits simulate the weather; 01-22 for rain, 23-33 for cloudy, 34-99 and 00 for sunny c. Two digits simulate the weather; 01-22 for rain, 23-32 for cloudy, 33-99 for sunny d. Two digits simulate the weather; 01-22 for rain, 23-32 for cloudy, 33-99 and 00 for sunny
d
