Chapter 1 - Chapter 10 Statistics

Statisticians often write the word​ _______ in front of the​ y-variable in the equation of the regression line.

"predicted"

A researcher carried out a hypothesis test using a​ two-tailed alternative hypothesis. Which of the following​ z-scores is associated with the smallest​ p-value? Explain. i. z=0.58 ii. z=1.48 iii. z=2.45 iv. z=3.05 Which​ z-score has the smallest​ p-value? A. z=3.05 B. z=1.48 C. z=2.45 D. z=0.58 Explain. A. The​ z-score farthest from 0 has the smallest tail area and thus has the smallest​ p-value. Your answer is correct. B. The​ z-score closest to 0 has the smallest tail area and thus has the smallest​ p-value. C. The​ z-score closest to 0 has the largest tail area and thus has the smallest​ p-value. D. The​ z-score farthest from 1 has the largest tail area and thus has the smallest​ p-value.

(a)(a)

State whether each of the following changes would make a confidence interval wider or narrower.​ (Assume that nothing else​ changes.) a. Changing from a 99​% confidence level to a 95​% confidence level. b. Changing from a sample size of 15 to a sample size of 250. c. Changing from a standard deviation of 20 pounds to a standard deviation of 30 pounds. LOADING... Click the icon to view the​ t-table. a. How will changing from a 99​% confidence level to a 95​% confidence level affect the width of the confidence​ interval? A. The interval will become narrower. B. The interval will become wider. C. This change will not affect the width of the interval. b. How will changing from a sample size of 15 to a sample size of 250 affect the width of the confidence​ interval? A. The interval will become narrower. B. The interval will become wider. C. This change will not affect the width of the interval. c. How will changing from a standard deviation of 20 pounds to a standard deviation of 30 pounds affect the width of the confidence​ interval?

(a)(a)(a)

A doctor who believes strongly that antidepressants work better than​ "talk therapy" tests depressed patients by treating half of them with antidepressants and the other half with talk therapy. After six months the patients are evaluated on a scale of 1 to​ 5, with 5 indicating the greatest improvement. Answer parts​ (a) through​ (d) below. a. The doctor is concerned that if his most severely depressed patients do not receive the​ antidepressants, they will get much worse. He therefore decides that the most severe patients will be assigned to receive the antidepressants. Explain why this will affect his ability to determine which approach works best. A. If the doctor decides on the​ treatment, this could introduce bias. B. The doctor is creating a second treatment group that is dependent on the severity of the​ patient's depression. This will further confound the results. C. The doctor is assigning all antidepressants to only the most severely depressed people. D. The doctor is letting his empathy get in the way of treating the patients objectively. This may cause personal issues for either the doctor or the patients over the course of the treatment. b. What advice would you give the doctor to improve his​ study? A. The doctor should randomly assign the patients to the different treatments. B. The doctor should divide the patients into groups based on how depressed they​ are, and give out a certain percentage of antidepressants to the least depressed​ group, a higher percentage to the more depressed​ group, and so on. C. The doctor must give an equal number of antidepressants to the least depressed patients and the most depressed patients in order to make the treatment sufficiently random. D. The doctor should remain as objective as possible in order to increase the chances of successfully treating the patients. E. The doctor should remove the least depressed people from the study. c. The doctor asks you whether it is acceptable for him to know which treatment each patient receives and to evaluate them himself at the end of the study to rate their improvement. Explain why this practice will affect his ability to determine which approach works best. A. If the doctor is aware of the treatment each patient​ receives, he may bribe the patients to skew the results in his favor. B. If the doctor is aware of the treatment each patient​ receives, it may negatively affect the relationship between the doctor and patient during therapy sessions. C. If the doctor is aware of the treatment each patient​ receives, that might influence his opinion about the effectiveness of the treatment. D. If the doctor is aware of the treatment each patient​ receives, he may become too invested in the​ well-being of the patients. d. What improvements to the plan in part​ (c) would you​ recommend? A. To prevent​ bias, the experiment should be​ double-blind. Neither the patients nor the doctor evaluating the patients should know whether each patient received medication. B. To prevent​ bias, the sample size should be increased to reduce the effect of his bias on the study. C. To prevent​ bias, the evaluation should be completed by another doctor in order to make the study as objective as possible. D. To prevent​ bias, the doctor should use an evaluation procedure that is resistant to bias.

(a)(a)(c)(a)

Indicate which variable you think should be the predictor​ (x) and which variable should be the response​ (y). Explain your choices. a. You have collected data on used cars for sale. The variables are price and odometer readings of the cars. b. Research is conducted on monthly household expenses. Variables are monthly water bill and household size. c. A personal trainer gathers data on the weights and time spent in the gym for each of her clients. a. Choose the correct choice below. A. The predictor is odometer reading. The response is price. Cars with higher mileage have been on the road​ longer, and have likely retained less of their original value. B. The predictor is price. The response is odometer reading. Cars that have retained more of their original value are more​ reliable, and have likely been on the road longer. C. The predictor is price. The response is odometer reading. Cars that have retained more of their original value are less​ reliable, and have likely been on the road for a shorter amount of time. D. The predictor is odometer reading. The response is price. Cars with higher mileage have been on the road​ longer, and have likely retained more of their original value. b. Choose the correct choice below. A. The predictor is household size. The response is monthly water bill. Larger households tend to use less water. B. The predictor is monthly water bill. The response is household size. Larger water bills tend to result in larger families. C. The predictor is monthly water bill. The response is household size. Larger water bills tend to result in smaller families. D. The predictor is household size. The response is monthly water bill. Larger households tend to use more water. c. Choose the correct choice below. A. The predictor is weight. The response is time spent in the gym. Clients with lower weights are less likely to have spent a large amount of time working out. B. The predictor is weight. The response is time spent in the gym. Clients with lower weights are more likely to have spent a large amount of time working out. C. The predictor is time spent in the gym. The response is weight. Clients who have spent more time working out are more likely to have lost weight. D. The predictor is time spent in the gym. The response is weight. Clients who have spent more time working out are less likely to have lost weight.

(a)(b)(c)

Determine whether each of the following variables would best be modeled as continuous or discrete. a. The number of characters typed per minute b. The number of socks in a drawer c. Blood sugar level d. The decibel level of a siren a. Is the number of characters typed per minute discrete or​ continuous? A. The variable is continuous. B. The variable is discrete. Your answer is correct. b. Is the number of socks in a drawer discrete or​ continuous? A. The variable is continuous. B. The variable is discrete. c. Is blood sugar level discrete or​ continuous? A. The variable is continuous. Your answer is correct. B. The variable is discrete. d. Is the decibel level of a siren discrete or​ continuous? A. The variable is continuous. B. The variable is discrete.

(b)(b)(a)(a)

A blog noted that​ "there has been increasing anecdotal evidence that vitamin C may still be useful as an anticancer medicine if used in high concentrations and given directly into the vein​ (intravenously)." Use this information to answer the questions below. Explain what it means that there is​ "increasing anecdotal​ evidence" that Vitamin C may be a useful anticancer medicine. A. There is no evidence that shows Vitamin C may be a useful anticancer medicine. B. There is an increase in observations or personal experiences that shows Vitamin C may be a useful anticancer medicine. C. There is an increase in rigorous or scientific analysis that shows Vitamin C may be a useful anticancer medicine. D. There is scientific evidence that Vitamin C is a​ non-useful anticancer medicine. How does anecdotal evidence contrast with scientific​ evidence? A. They are always more accurate than scientific evidence. B. They are stories about multiple cases. C. They are stories about individual cases. D. They have the strongest strength of evidence out of all types of evidence. What kind of​ conclusions, if​ any, can be made from anecdotal​ evidence? A. No​ cause-and-effect conclusions can be drawn from anecdotal evidence because there could be other outside factors related to Vitamin C and cancer influencing the results. B. ​Cause-and-effect conclusions can be drawn from anecdotal evidence because the evidence clearly shows a​ one-way relationship. C. No​ cause-and-effect conclusions can be drawn from anecdotal evidence because​ cause-and-effect conclusions can never be drawn no matter the situation.

(b)(c)(a)

A friend is tested to see whether he can tell bottled water from tap water. There are 50 trials​ (half with bottled water and half with tap​ water), and he gets 28 right. a. Determine the null hypothesis. b. Determine the alternative hypothesis. a. Choose the correct answer below. A. p=0.56 B. p=0.50 C. p=0.56 D. p=0.50 b. Choose the correct answer below. A. p≠0.50 B. p≠0.56 C. p=0.56 D. p>0.50

(b)(d)

A researcher carried out a hypothesis test using a​ two-tailed alternative hypothesis. Which of the following​ z-scores is associated with the smallest​ p-value? Explain. i. z=−0.28 ii. z=1.09 iii. z=−2.39 iv. z=−3.37 Which​ z-score has the smallest​ p-value? A. z=−0.28 B. z=−3.37 C. z=−2.39 D. z=1.09 Explain. A. The​ z-score farthest from 1 has the largest tail area and thus has the smallest​ p-value. B. The​ z-score closest to 0 has the smallest tail area and thus has the smallest​ p-value. C. The​ z-score closest to 0 has the largest tail area and thus has the smallest​ p-value. D. The​ z-score farthest from 0 has the smallest tail area and thus has the smallest​ p-value.

(b)(d)

Suppose it is known that 29​% of students at a certain college participate in a textbook recycling program each semester. Complete parts​ (a) and​ (b) below. a. If a random sample of 70 students is​ selected, do we expect that exactly 29​% of the sample participates in the textbook recycling​ program? Why or why​ not? Choose the correct answer below. A. We expect that exactly 29​% of the sample participates in the textbook recycling​ program, because that is the percentage of students that participate in the program regardless of sample or population size. B. We do not expect that exactly 29​% of the sample participates in the textbook recycling program. 29​% is a population statistic and you cannot know anything about a sample from the population. C. We do not expect that exactly 29​% of the sample participates in the textbook recycling program. We do expect that the sample proportion will be close to the population​ proportion, but it will vary by the sample error from sample to sample. D. We expect that exactly 29​% of the sample participates in the textbook recycling​ program, because a sample always has the same statistics as the population. b. Suppose we take a sample of 700 students and find the sample proportion participating in the recycling program. Which sample proportion do you think is more likely to be closer to 29​%: the proportion from a sample size of 70 or the proportion from a sample size of 700​? Explain your reasoning. Choose the correct answer below. A. The sample with size 700 will be closer to 29​% because a larger sample size has a smaller standard error. B. The sample with size 70 will be closer to 29​% because a smaller sample size has less variation. C. The sample with size 700 will be closer to 29​% because a larger sample size has more variation. D. The sample with size 70 will be closer to 29​% because a smaller sample size has a smaller standard error.

(c) (a)

A coin will be flipped three​ times, and the number of heads recorded. Explain why this is a binomial experiment. Check all four required conditions. Determine whether there is a fixed number of​ trials, n. A. There is not a fixed number of​ trials, n. A certain number of heads must occur before the person can stop flipping the coin. B. There is a fixed number of​ trials, n. The number of times a heads or tails will occur is less than three. C. There is a fixed number of​ trials, n. The coin will be flipped three​ times, which is a fixed number. D. There is not a fixed number of​ trials, n. The number of times a heads or tails will occur is not determined prior to the set of coin flips. Determine whether the only two outcomes are success and failure. A. The only two outcomes are success and failure. In this​ experiment, three heads is considered a​ success, and fewer than three heads is considered a failure. B. There are six possible outcomes. There are three​ trials, and in each​ trial, there are two sides on which the coin could​ land, heads and tails. C. There are more than two possible outcomes. Flipping three heads in a row is an alternative definition of success. D. The only two outcomes are success and failure. In this​ experiment, a heads is considered a​ success, and a tails is considered a failure. Determine whether the probability of​ success, p, is the same at each trial. A. The probability of​ success, p, is not the same at each trial. The probability of flipping heads is either 0 or​ 1, because the outcome is either a heads or a tails. B. The probability of​ success, p, is not the same at each trial. Depending on the method of flipping the​ coin, the probability of flipping heads can change. C. The probability of​ success, p, is the same at each trial. The probability of flipping heads is always​ 0.5, minus the possibility of the coin landing on tails. D. The probability of​ success, p, is the same at each trial. The probability of flipping heads is always 0.5. Determine whether the trials are independent. A. The trials are independent. The result of any flip is independent of the result of the other flips. Your answer is correct. B. The trials are not independent. Flipping a heads affects the way the person will flip the coin in the next​ trial, which changes the probability of possible outcomes. C. The trials are independent. Since the coin is​ fair, the probability of heads is equal to the probability of​ tails; this equality holds only for independent trials. D. The trials are not independent. Whether a heads or tails will be flipped is​ pre-determined. Each trial is dependent on the overall order of the flips.

(c)(d)(d)(a)

Suppose a person is selected at random from a large population. a. Label each pair of events as mutually exclusive or not mutually exclusive. i. The selected person has brown eyes​; the selected person is married. ii. The selected person is an airline pilot​; the selected person is 8 years old. b. Give an example of two events that are mutually exclusive when a person is selected at random from a large population. a. i. Choose the correct answer below. A. The events are mutually exclusive because if one event occurs the probability of the second event occurring changes. B. The events are mutually exclusive because if one event occurs the other event cannot occur. C. The events are not mutually exclusive because if one event occurs the probability of the second event occurring changes. D. The events are not mutually exclusive because if one event occurs the other event can also occur. a. ii. Choose the correct answer below. A. The events are not mutually exclusive because if one event occurs the probability of the second event occurring changes. B. The events are mutually exclusive because if one event occurs the probability of the second event occurring changes. C. The events are mutually exclusive because if one event occurs the other event cannot occur. D. The events are not mutually exclusive because if one event occurs the other event can also occur. b. Choose the correct answer below. A. The selected person is single​; the selected person is a racecar driver B. The selected person has blond hair​; the selected person is a truck driver C. The selected person is 48 years old​; the selected person is president D. The selected person has blue eyes​;

(d)(c)(d)

The intercept of a regression line tells a person the predicted mean​ y-value when the​ x-value is​ _______.

0

Probabilities are always numbers between and including what​ numbers? Choose the correct answer below. 0 and 1 −1 and 1 0.01 and 1.0 1 and 100

0 and 1

As a rule of​ thumb, when considering whether or not to apply the Central Limit Theorem to a sample drawn from a population that is not​ normal, what sample size is considered​ "large"? Choose the correct answer below. 15 or more 25 or more 10 or more 50 or more

25 or more

Fill in the blank below. In order to do a​ goodness-of-fit hypothesis​ test, the expected count in each cell must be at least​ ____.

5

Fill in the blank below. The​ chi-square distribution provides a good approximation to the sampling distribution of the​ chi-square statistic if the expected count in each cell is​ _____.

5 or higher.

In order to conduct a hypothesis test for homogeneity or​ independence, what must the expected count in each cell​ be? Choose the correct answer below. 25 or more 10 or more 5 or more Less than 5

5 or more

Fill in the blank. The symbol in the null hypothesis is always​ _______.

=

How does one calculate the standard error of the sample​ means? Choose the correct answer below. A. Divide the population standard deviation by the square root of the sample size. B. Multiply the population standard deviation by the square root of the sample size. C. Divide the square root of the sample size by the population standard deviation. D. Divide the population standard deviation by the sample size.

A

In hypothesis​ testing, the null hypothesis is best described by which of the following​ statements? Choose the correct answer below. A. The null hypothesis always gets the benefit of the doubt and is assumed to be true throughout the hypothesis testing procedure. B. The null hypothesis is always assumed to be false throughout the hypothesis testing procedure. C. The null hypothesis can be chosen by a computer. D. Both A and C are correct

A

Is it acceptable practice to look at your research​ results, note the direction of the​ difference, and then make the alternative hypothesis​ one-sided in order to achieve a significant​ difference? Explain. Choose the correct answer below. A. No. Changing the alternative hypothesis is considered cheating. B. Yes. This is only unacceptable when changing from a​ one-sided alternative hypothesis to a​ two-sided hypothesis. C. Yes. The alternative hypothesis must be as accurate as possible. D. No. This is only acceptable when changing from a​ one-sided alternative hypothesis to a​ two-sided hypothesis.

A

The mean GPA of all 3000 students at a college is 2.41. A sample of 50 GPAs from this school has a mean of 2.95. Which number is μ and which is x​? Choose the correct answer below. A. The population mean is μ=2.41​, and the sample mean is x=2.95. B. The population mean is x=2.41​, and the sample mean is μ=2.95. C. The statistic is μ=2.41​, and the parameter is x=2.95. D. The statistic is x=2.41​, and the parameter is μ=2.95.

A

The null hypothesis on​ true/false tests is that the student is​ guessing, and the proportion of right answers is 0.50. A student taking a​ five-question true/false quiz gets 4 right out of 5. She says that this shows that she knows the​ material, because the​ one-tailed p-value from the​ one-proportion z-test is​ 0.090, and she is using a significance level of 0.10. What is wrong with her​ approach? Choose the correct answer below. A. The sample size is not large enough to use the​ one-proportion z-test. To use that​ test, the tester must expect at least 10 successes and at least 10 failures. B. The student used a hypothesis test instead of a confidence interval. A confidence interval would show the range of possible values for her proportion of correct answers. If this interval does not include​ 0.50, there would be evidence she knows the material. C. The student is conflating statistical significance with practical significance. If her true proportion of correct answers​ is, say,​ 0.52, this does not show that she knows the material. D. The student calculated the​ p-value incorrectly. The​ p-value in this case is actually 0.910.

A

What is the mean of the sampling distribution of the sample​ mean? Choose the correct answer below. A. The population mean B. The population standard deviation C. The population standard deviation divided by the square root of the sample size D. The sample standard deviation

A

When computing the​ t-statistic, one divides by an estimate of the standard error. Why does one not divide by the true standard​ error? Choose the correct answer below. A. Because in real life one almost never knows the value of the population standard deviation. B. Because this saves time and makes the calculation easier to do. C. Because in real life one almost never knows the value of the population mean. D. Because this gives one a more accurate value for the​ t-statistic.

A

When should a confidence interval approach be​ used? Choose the correct answer below. A. Whenever one is estimating the value of a population parameter on the basis of a random sample from that population. B. Whenever one is testing the validity of a hypothesis. C. Whenever the population mean is known. D. All of the above

A

Which of the following is an appropriate interpretation of a confidence​ interval? Choose the correct answer below. A. A range of plausible values for the population parameter. B. The interval in which the population parameter is certain to fall. C. A range of plausible values for the sample statistic. D. The probability that a population parameter falls in a certain range of values.

A

Which of the following is an appropriate interpretation of the confidence​ level? Choose the correct answer below. A. It is a measure of how well the method used to produce the confidence interval performs. B. It is a probability that the confidence interval is accurate. C. It is a measure of how strong the evidence is that the null hypothesis is true. D. It is the probability that the population parameter is contained in the confidence interval.

A

A magazine advertisement claims that wearing a magnetized bracelet will reduce arthritis pain in those who suffer from arthritis. A medical researcher tests this claim with 233 arthritis sufferers randomly assigned to wear either a magnetized bracelet or a placebo bracelet. The researcher records the proportion of each group who report relief from arthritis pain after 6 weeks. After analyzing the​ data, he fails to reject the null hypothesis. What are valid interpretations of his​ findings? Which of the following are valid interpretations of his​ findings? There may be more than one correct answer. Select all answers that apply. A. There were no statistically significant differences between the magnetized bracelets and the placebos in reducing arthritis pain. B. ​There's insufficient evidence that the magnetized bracelets are effective at reducing arthritis pain. C. The magnetized bracelets are not effective at reducing arthritis pain. D. The magnetized bracelets had exactly the same effect as the placebo at reducing arthritis pain.

A and B

A difference between two groups in an observational study that can explain why the outcomes were very different between the groups is called​ what? Choose the correct answer below. A treatment variable An outcome variable A causality A confounding variable

A confounding variable

Which of the following cannot be used to represent a discrete probability​ distribution? Choose the correct answer below. Equations Tables Areas under curves Graphs

Areas under curves

Which of the following is used to summarize two potentially related categorical​ variables? A​ two-way table Stacked table Frequency table Histogram

A​ two-way table

A 2003 study of dreaming found that out of a random sample of 114 ​people, 83 reported dreaming in color.​ However, the rate of reported dreaming in color that was established in the 1940s was 0.22. Check to see whether the conditions for using a​ one-proportion z-test are met assuming the researcher wanted to test to see if the proportion dreaming in color had changed since the 1940s. Are the conditions​ met? A. ​No, the observations are not independent. B. ​Yes, all the conditions are met. C. ​No, the population is not more than 10 times bigger than the sample size. D. ​No, the sample size is not large enough to produce at least 10 successes and 10 failures.

B

A confidence interval answers which of the following​ questions? Choose the correct answer below. A. Is the​ parameter's value one thing or​ another? B. What is the estimated value and how much uncertainty does one have in this​ estimate? C. Both A and B are correct D. None of the above

B

A random sample of 10 colleges was taken. A​ 95% confidence interval for the mean admission rate was (52.8%, 75.0%). The rates of admission were Normally distributed. Which of the following statements is the correct interpretation of the confidence level​, and which is the correct interpreation of the confidence interval​? a. We are confident that the mean admission rate is between​ 52.8% and​ 75.0%. b. In about​ 95% of all samples of 10​ colleges, the confidence interval will contain the population mean admission rate. Select the correct answer below. A. Statement​ (a) correctly interprets the confidence level and statement​ (b) correctly interprets the confidence interval. B. Statement​ (b) correctly interprets the confidence level and statement​ (a) correctly interprets the confidence interval.

B

If we do not reject the null​ hypothesis, is it valid to say that we accept the null​ hypothesis? Why or why​ not? Choose the correct answer below. A. ​Yes, because the null and alternative hypotheses are opposites. If the alternative hypothesis is​ rejected, the null hypothesis must be accepted. B. ​No, we have only shown that we do not have enough evidence to reject it. C. ​No, a second sample must be taken and tested first to confirm the results of the first test. D. ​Yes, and it would even be valid to say we have proved the null hypothesis.

B

If we reject the null​ hypothesis, can we claim to have proved that the null hypothesis is​ false? Why or why​ not? Choose the correct answer below. A. ​Yes, if the test conditions are satisfied and the​ p-value is smaller than the significance​ level, then the null hypothesis is proven to be false. B. ​No; we​ don't use prove because we cannot be​ 100% sure of conclusions based on chance processes. C. Not​ necessarily, if the test conditions are satisfied and the​ p-value is appropriately​ small, the null hypothesis can only be proven false if the significance level is appropriately small. D. Not​ necessarily, if the test conditions are satisfied and the​ p-value is appropriately​ small, the null hypothesis can only be proven false if the power is appropriately large.

B

In hypothesis​ testing, when should the null hypothesis be​ rejected? Choose the correct answer below. A. When the​ p-value is greater than the value in the null hypothesis B. When the​ p-value is less than the significance level C. When the​ p-value is greater than the significance level D. When the​ p-value is less than the value in the null hypothesis

B

The results of a study are said to be replicable when which of the following is​ true? Choose the correct answer below. A. Results can be used to establish a​ cause-and-effect relationship B. Researchers using new subjects come to the same conclusion C. The test statistic resulting from the test was not extreme D. The​ p-value led researchers to reject the null hypothesis

B

What is one indication that there are paired samples in a data​ set? Choose the correct answer below. A. The researcher is working with two distinct groups in the data set. B. Each observation in one group is coupled with one particular observation in the other group. C. Knowing the value that a subject has in one group gives one no information about the value in the second group. D. The researcher is comparing two populations.

B

What is true of the shape of a binomial​ distribution? Choose the correct answer below. A. The shape never changes. B. The shape depends on both the number of​ trials, n, and the probability of​ success, p. C. The shape depends solely on the probability of​ success, p. D. The shape depends solely on the number of​ trials, n.

B

Which of the following is measured by the test​ statistic? Choose the correct answer below. A. How far away the observed mean lies from the true population mean. B. How far away the observed mean lies from the hypothesized value of the population mean. C. The probability that the hypothesized mean is correct. D. The level of confidence one has in our conclusion.

B

Which of the following is not a condition that must be checked before applying the Central Limit​ Theorem? Choose the correct answer below. A. Either the population distribution is Normal or the sample size is large B. The samples must be drawn from a population that is Normal. C. The population must be at least 10 times larger than the sample size if the sample is collected without replacement D. Each sample is collected randomly and the observations are independent.

B

While the majority of people who are color blind are​ male, an institute reports that 0.7​% of women with Northern European ancestry have the common form of​ red-green color blindness. Suppose a random sample of 150 women with Northern European ancestry is selected. Can we find the probability that less than 0.6​% of the sample is color​ blind? If​ so, find the probability. If​ not, explain why this probability cannot be calculated. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. This probability cannot be calculated because the sample does not satisfy the Central Limit Theorems conditions for randomness and independence. B. This probability cannot be calculated because the sample is too small to satisfy the conditions of the Central Limit Theorem. C. This probability can be​ calculated, the sample meets all of the conditions of the Central Limit Theorem. The probability is enter your response here​%. ​(Type an integer or decimal rounded to one decimal place as​ needed.) D. This probability can be​ calculated, the sample meets enough of the conditions of the Central Limit Theorem. The probability is enter your response here​%. ​(Type an integer or decimal rounded to one decimal place as​ needed.) E. This probability cannot be calculated because the population size is too small to satisfy the conditions of the Central Limit Theorem.

B

Why are percentages or rates often better than counts for making​ comparisons? A. They are more statistically significant than counts. B. They take into account possible differences among the sizes of the groups. C. They are more accurate than counts. D. Percentages are better than counts when there is categorical data.

B

s simple random sampling usually done with or without​ replacement? Choose the correct answer below. A. Simple random sampling is usually done with​ replacement, which means that a subject can be selected for a sample more than once. B. Simple random sampling is usually done without​ replacement, which means that a subject cannot be selected for a sample more than once. C. Simple random sampling is usually done with​ replacement, which ensures that unbiased samples are more likely to be chosen than biased samples of the same size. D. Simple random sampling is usually done without​ replacement, which ensures that unbiased samples are more likely to be chosen than biased samples of the same size.

B

​When, in a criminal​ court, a defendant is found​ "not guilty," is the court saying with certainty that he or she is​ innocent? Explain. Choose the correct answer below. A. ​Yes, because the only options for a decision are​ "guilty" and​ "innocent." Finding the defendant​ "not guilty" is the same as finding the defendant innocent. B. ​No, the court is only saying that there is not enough evidence to show guilt. C. ​No, the court is asking for a second trial. D. ​No, the court is saying the jury is unable to reach a definitive conclusion.

B

A confidence interval communicates an estimate of the mean and also which of the​ following? Choose the correct answer below. A. The sample size that was used to make the estimate B. An estimate of the standard deviation C. A measure of​ one's uncertainty in the estimate D. All of the above

C

In order to measure the job performance of a confidence​ interval, which of the following is not a condition that must be​ checked? Choose the correct answer below. A. Either the population must be Normally distributed or the sample size must be at least 25. B. The data must be collected randomly and each observation must be independent. C. The population size must not be larger than 10 times the sample size. D. All of these conditions must be checked.

C

To measure the quality of a​ survey, statisticians evaluate which of the​ following? Choose the correct answer below. A. The population being measured B. The outcome of the survey C. The method used for the survey D. All of the above

C

What does a probability distribution​ indicate? Choose the correct answer below. A. The probability of each outcome of a random experiment B. All the possible outcomes of a random experiment C. Both A and B D. None of the above

C

What should be done to create a confidence interval for a population​ proportion? Choose the correct answer below. A. Multiply the margin of error and the sample proportion B. Subtract the margin of error from the sample proportion C. Add and subtract the margin of error​ to/from the sample proportion D. Add the margin of error to the sample proportion

C

When a person stands trial for​ murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null​ hypothesis, or is it an example of an alternative​ hypothesis? Choose the correct answer below. A. It is an alternative​ hypothesis, since it is assumed to be false until evidence can prove otherwise. B. It is an alternative​ hypothesis, since it is assumed to be true until evidence can prove otherwise. C. It is a null​ hypothesis, since it is assumed to be true until evidence can prove otherwise. D. It is a null​ hypothesis, since it is assumed to be false until evidence can prove otherwise.

C

When taking samples from a population and computing the proportion of each​ sample, which of the following values is always the​ same? Choose the correct answer below. A. The sample proportion B. The accuracy of each sample proportion in estimating the population proportion C. The population proportion D. All of the above

C

Which of the following phrases should not be used when writing a conclusion to a hypothesis​ test? Choose the correct answer below. A. Fail to reject the null hypothesis. B. The null hypothesis cannot be rejected. C. The null hypothesis is accepted as true. D. All of the above are correct ways of writing a hypothesis test conclusion.

C

Probabilities where the focus is on just one group of objects and a random sample is taken from that group alone are called​ what? Choose the correct answer below. Conditional probabilities Mutually exclusive probabilities Random probabilities Categorical probabilities

Conditional probabilities

What are numerical variables with outcomes that cannot be listed or counted because they occur over a range​ called? Choose the correct answer below. Normal Continuous Probable Discrete

Continuous

How are confidence intervals reported by professional statisticians and the​ press? Choose the correct answer below. A. Estimate ± margin of error B. ​(lower boundary, upper​ boundary) C. Using just the estimator D. Both A and B

D

If the conditions of a survey sample satisfy those required by the Central Limit​ Theorem, then there is a​ 95% probability that a sample proportion will fall within how many standard errors of the population​ proportion? Choose the correct answer below. A. 1 standard error B. 3 standard errors C. 1.5 standard errors D. 2 standard errors

D

Suppose you attend a school that offers both traditional courses and online courses. You want to know the average age of all the students. You walk around campus asking those students that you meet how old they are. Would this result in an unbiased​ sample? Choose the correct answer below. A. ​Yes, since this sample is random and samples from the entire population. B. ​No, since a relatively large number of students may refuse to respond or lie when asked about their age. C. ​No, since students themselves choose to participate in the​ survey, resulting in response bias. D. ​No, since this method will not select people who take online classes but may have a different mean age than the traditional students.

D

Suppose​ that, when taking a random sample of three​ students' GPAs, you get a sample mean of 3.90. This sample mean is far higher than the​ college-wide (population) mean. Does this prove that your sample is​ biased? Explain. What else could have caused this high​ mean? Choose the correct answer below. A. One or more of the students could have lied about their GPAs. B. The sample may not be biased. The measurements may not have been precise. C. Nothing other than bias could have caused this small mean. D. The sample may not be biased. The high mean might have occurred by​ chance, since the sample size is very small.

D

When a confidence interval for the difference of two population means contains​ 0, what can be​ concluded? Choose the correct answer below. A. The results of the confidence interval are inconclusive. B. An error was made in the calculation. C. The population means are significantly different. D. The population means may be the same.

D

When is a method called​ "biased"? Choose the correct answer below. A. It is difficult to use. B. It always produces an untrue value. C. It is complicated to carry out. D. It has a tendency to produce an untrue value.

D

Which of the following is not a characteristic that must be present in a binomial​ model? Choose the correct answer below. A.term-29 The probability of success is the same at each trial. B. There is a fixed number of trials. C. There are only two outcomes for each trial. D. The trials are dependent.

D

Which of the following is not a condition to check when doing a​ two-sample z-test of​ proportions? Choose the correct answer below. A. The samples are independent of each other and independent within samples B. The samples are sufficiently large C. The sample are random D. All of the above conditions are important conditions to check

D

The binomial probability model is useful in many situations with variables of what​ kind? Choose the correct answer below. Categorical variables ​Continuous-valued numerical variables ​Discrete-valued numerical variables Both​ discrete-valued and​ continuous-valued variables

Discrete-valued numerical variables

A psychologist is interested in testing whether offering students a financial incentive improves their​ video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video game is greater with a financial incentive than without. Her null hypothesis is that the probability of getting to this level is the same with or without a financial incentive. The alternative is that this probability is greater. She gets a​ p-value from her hypothesis test of 0.003. What is the best interpretation of the​ p-value? Which of the following is the best interpretation of the​ p-value? Choose the correct answer below. A. The​ p-value is the probability of getting a result as extreme as or more extreme than the one​ obtained, assuming that financial incentives are effective in this context. B. The​ p-value is the probability that financial incentives are not effective in this context. C. The​ p-value is the probability of getting exactly the result​ obtained, assuming that financial incentives are not effective in this context. D. The​ p-value is the probability of getting exactly the result​ obtained, assuming that financial incentives are effective in this context. E. The​ p-value is the probability of getting a result as extreme as or more extreme than the one​ obtained, assuming that financial incentives are not effective in this context.

E

Probabilities that are based on​ short-run relative frequencies are called​ what? Choose the correct answer below. Theoretical probabilities Empirical probabilities Practical probabilities Pseudo probabilities

Empirical probabilities

Does establishing a small value for the significance level guard against the first type of error​ (rejecting the null hypothesis when it is​ true) or guard against the second type of​ error?

Establishing a small value for the significance level guards against the first type of error because a smaller significance level makes it harder to reject the null hypothesis.

What are the two tests that can be used to determine if there is an association between categorical​ variables? Choose the correct answer below. Homogeneity and dependence Homogeneity and heterogeneity Homogeneity and independence Dependence and independence

Homogeneity and independence

Variables or events that are not associated are called​ what? Choose the correct answer below. Dependent Categorical Random Independent

Independent

When two events have no outcomes in​ common, they are called​ what? Choose the correct answer below. Conditional A sample space Complementary Mutually exclusive

Mutually exclusive

Hypotheses are always statements about which of the​ following? Choose the correct answer below. Sample statistics Sample size Population parameters Estimators

Population parameters

Fill in the blank. A useful estimator for the population mean is the​ _______.

Sample mean

What is the standard deviation of the sampling distribution​ called? Choose the correct answer below. Precision Standard error Bias Sampling error

Standard error

If an experiment with a random outcome is repeated a large number of​ times, the empirical probability of an event is likely to be close to the true probability. This mathematical theorem is called​ what? Choose the correct answer below. The Law of Binomial Probability The Random Number Table The Law of Simulation The Law of Large Numbers

The Law of Large Numbers

What is the most widely used probability model for continuous numerical​ variables? Choose the correct answer below. The Central Limit Theorem The unimodal distribution The probability density function The Normal distribution

The Normal distribution

Suppose you are testing someone to see whether he or she can tell butter from margarine when it is spread on toast. You use many​ bite-sized pieces selected​ randomly, half from buttered toast and half from toast with margarine. The taster is blindfolded. The null hypothesis is that the taster is just guessing and should get about half right. When you reject the null hypothesis when it is actually​ true, that is often called the first kind of error. The second kind of error is when the null is false and you fail to reject. Report the first kind of error and the second kind of error.

The first kind of error is saying the person can tell butter from margarine when in fact he or she cannot. The second kind of error is saying the person cannot tell butter from margarine when in fact he or she can.

Sir William Blackstone ​(1723-​1780) wrote influential books on common law. He made the statement​ "All presumptive evidence of felony should be admitted​ cautiously; for the law holds it better that ten guilty persons escape​, than that one innocent party suffer​." Keep in mind that the null hypothesis in criminal trials is that the defendant is not guilty. State which of these errors​ (in bold) is the first type of error​ (rejecting the null hypothesis when it is actually​ true) and which is the second type of error.

The first type of error is having the innocent person suffer and the second type of error is having ten guilty persons escape.

What is another name for the expected value of a probability​ distribution? Choose the correct answer below. The shape of the distribution The standard deviation The mean The variability of the distribution

The mean

Suppose you are spinning pennies to test whether you get biased results. When you reject the null hypothesis when it is actually​ true, that is often called the first kind of error. The second kind of error is when the null is false and you fail to reject. Report the first kind of error and the seconterm-8d kind of error.

The null hypothesis is that the penny is not biased. The first kind of error is saying the penny is biased when in fact the penny is not biased. The second kind of error is saying the penny is not biased when in fact the penny is biased.

The outcome variable in a question about causality is also referred to as​ what? Choose the correct answer below. The predicting variable The control group The response variable The treatment variable

The response variable

What determines the exact shape of a Normal​ distribution? Choose the correct answer below. The value of the mean and median The values of the mean and the standard deviation Your answer is correct. The value of the mean The value of the standard deviation

The values of the mean and the standard deviation

The multiplier used to compute the margin of error for a confidence interval for a population mean is based on which of the​ following? Choose the correct answer below. The Normal distribution The​ t-distribution The value of the estimator The Standard Normal distribution

The​ t-distribution

A large number of surgery patients get infections after​ surgery, which can sometimes be quite serious. Researchers randomly assigned some surgery patients to receive a simple antibiotic ointment after​ surgery, others to receive a​ placebo, and others to receive just cleansing with soap. If we wanted to test the association between treatment and whether or not patients get an infection after​ surgery, would this be a test of homogeneity or of​ independence? Explain. Choose the correct answer beloew. A. It would be a test of homogeneity because the patients were randomly assigned to different groups. B. It would be a test of independence because there was only one sample. C. It would be a test of independence because the patients are being separated into more than two categories after being asked the question. D. It would be a test of homogeneity because there was only one sample.

a

A research organization keeps track of what citizens think is the most important problem facing the country today. They randomly sampled a number of people in 2003 and again in 2009 using a different random sample of people in 2009 than in 2003 and asked them to choose the most important problem facing the country today from the following​ choices, war,​ economy, health​ care, or other. Which of the following is the correct test to use to determine if the distribution of​ "problem facing this country​ today" is different between the two different​ years? Choose the correct answer below. A. Use a​ chi-square test of homogeneity. B. Use a paired​ t-test. C. Use a​ chi-square goodness-of-fit test. D. Use a​ two-sample z-test for proportions.

a

In a hypothesis test to determine if there is an association between two categorical​ variables, what can be said about the null​ hypothesis? Choose the correct answer below. A. The null hypothesis always states that there is no association between the variables. B. The null hypothesis always states that there is an association between the variables. C. The null hypothesis always contains an equals sign. D. The null hypothesis changes depending on the context of the problem.

a

Indicate whether the study is an observational study or a controlled experiment. Patients with multiple sclerosis are randomly assigned a new drug or placebo and are then given a test of coordination after six months. Choose the correct answer below. A. This is a controlled experiment because the patients were assigned drugs by those conducting the study. B. This is a controlled experiment because the patients chose whether they took the drug or the placebo. C. This is an observational study because the patients chose whether they took the drug or the placebo. D. This is an observational study because the patients were assigned drugs by those conducting the study.

a

Suppose a person is chosen at random. Use your understanding about football to decide whether the event that the person weighs more than 300 pounds and the event that the person plays professional football are independent or associated. Choose the correct answer below. A. The two events are associated because professional football players are more likely to be weigh more than 300 pounds than the average person. B. The two events are independent because they are mutually exclusive events. C. The two events are independent because professional football players are just as likely to be weigh more than 300 pounds than the average person. D. The two events are independent because the outcome of one does not affect the outcome of the other.

a

The correlation between height and arm span in a sample of adult women was found to be r=0.936. The correlation between arm span and height in a sample of adult men was found to be r=0.866. Which association—the association between height and arm span for​ women, or the association between height and arm span for men—is ​stronger? Explain. Choose the correct answer below. A. The association between height and arm span for women is stronger because the value of r is farther from 0. B. The association between height and arm span for men is stronger because the value of r is closer to 0. C. The association between height and arm span for men is stronger because the value of r is farther from 0. D. The association between height and arm span for women is stronger because the value of r is closer to 0.

a

Which of the following is always the null hypothesis for a​ goodness-of-fit test? Choose the correct answer below. A. The population distribution of the variable is the same as the proposed distribution. B. The null hypothesis varies depending on the context. C. The population distribution of the variable is different from the proposed distribution. D. The means of the distributions are equal.

a

State whether each situation has independent or paired​ (dependent) samples. a. A researcher wants to know whether men and women at a particular amusement park have different mean cholesterol levels. She gathers two random samples​ (one of cholesterol levels from 100 men and the other from 100 ​women.) b. A researcher wants to know whether twins have different mean cholesterol levels. He collects a sample of twins and has each person report his or her cholesterol level. a. Choose the correct answer below. Independent samples Your answer is correct. Paired​ (dependent) samples b. Choose the correct answer below. Paired​ (dependent) samples Your answer is correct. Independent samples

a. is independent samples b. is paired (dependent) samples

Indicate whether the study is an observational study or a controlled experiment. A student watched picnickers with a large cooler of soft drinks to see whether teenagers were less likely than adults to choose diet soft drinks over regular soft drinks. The study is ...

an observational study

A December 2009 poll asked a random sample of people whether they thought their country was heading in the right direction. Each respondent answered​ "Right Direction" or​ "Wrong Direction" and was classified as​ Republican, Democrat, or Independent. If we were interested in testing whether party affiliation was associated with the answer to the​ question, would this be a test of homogeneity or of​ independence? Explain. Choose the correct answer below. A. It would be a test of independence because the people are being separated into more than two categories after being asked the question. B. It would be a test of independence because there was only one sample. C. It would be a test of homogeneity because the people are being separated into more than two categories after being asked the question. D. It would be a test of homogeneity because there was only one sample.

b

A Monopoly player claims that the probability of getting a 4 when rolling a​ six-sided die is 16 because the die is equally likely to land on any of the six sides. Is this an example of a theoretical probability or an empirical​ probability? Explain. Choose the correct answer below. A. This is an example of theoretical probability because it is based on an experiment. B. This is an example of theoretical probability because it is not based on an experiment. C. This is an example of empirical probability because it is based on the relative frequency at which an event happens after infinitely many repetitions. D. This is an example of empirical probability because it is based on an experiment.

b

A person was trying to figure out the probability of getting two heads when flipping two coins. She flipped two coins 25 ​times, and in 7 of these 25 ​times, both coins landed heads. On the basis of this​ outcome, she claims that the probability of two heads is 7​/25​, or 28​%. Is this an example of an empirical probability or a theoretical​ probability? Explain. Choose the correct answer below. A. This is an example of empirical probability because it is based on the relative frequency at which an event happens after infinitely many repetitions. B. This is an example of empirical probability because it is based on an experiment. C. This is an example of theoretical probability because it is based on an experiment. D. This is an example of theoretical probability because it is not based on an experiment

b

Given the event​ "a die lands with a 6 on​ top", which of the following is the complement of this​ event? Choose the correct answer below. A. The die lands with a 6 on the bottom B. The die lands with a​ 1, 2,​ 3, 4, or 5 on top C. The die lands with a 3 on the top D. The number of times the die lands with a 6 on top in n throws of the die

b

If a professor adds 10 points to each​ student's final exam​ score, how will it affect the distribution of final exam​ scores? Choose the correct answer below. A. The spread will​ change, but the center and shape will remain the same. B. The center will​ change, but the shape and spread will remain the same. C. The center and spread will​ change, but the shape will remain the same. D. The​ center, shape, and spread will all change.

b

If all the data values in a set are​ identical, what can you conclude about the standard​ deviation? Choose the correct answer below. A. The standard deviation is equal to the data value. B. The standard deviation is zero. C. The standard deviation is not defined if all the data values are identical. D. The standard deviation cannot be calculated without knowing the value in the data set.

b

If the probability that it will rain tomorrow is​ 0.30, the probability that it will not rain tomorrow is​ what? Choose the correct answer below. A. 0.30 B. 0.70 C. −0.30 D. Impossible to determine from the given information

b

If there is a positive correlation between number of years studying grammar and tongue length ​(for children), does that prove that a longer tongue causes more studying of grammar​, or vice​ versa? Can you think of a hidden variable that might be influencing both of the other​ variables? Choose the correct answer below. A. It does not prove​ causation, because older children have a longer tongue and have studied grammar longer. A longer tongue does not cause an increase in years of studying. There is no hidden variable. B. It does not prove​ causation, because older children have a longer tongue and have studied grammar longer. A longer tongue does not cause an increase in years of studying. The hidden variable is age. C. It proves​ causation, because the two variables are related implying causation. A longer tongue causes an increase in years of studying. The hidden variable is age. D. It proves​ causation, because the two variables are related implying causation. A longer tongue causes an increase in years of studying. There is no hidden variable.

b

If there is no association between the categorical​ variables, then which of the following must be​ true? Choose the correct answer below. A. The​ chi-square statistic will have a large value. B. The observed counts in the​ two-way table should be close to the expected counts. C. The​ chi-square statistic will have a large value and the observed counts in the​ two-way table will be very different from the expected counts. D. The observed counts in the​ two-way table will be very different from the expected counts.

b

Indicate whether the following study is an observational study or a controlled experiment. A local public school​ encourages, but does not​ require, students to wear uniforms. The principal of the school compares the grade point averages of students at this school who wear uniforms with the GPAs of those who do not wear uniforms to determine whether those wearing uniforms tend to have higher GPAs. Select the correct answer below. A. This is a controlled experiment. The principal does not actually observe any characteristics of the​ students; the only data collected are the GPAs of the students. Observation in a natural environment is essential to conducting an observational study. B. This is an observational study. The principal does not randomly assign students to either wear or not wear uniforms. Random assignment is essential to conducting a controlled experiment. C. This is a controlled experiment. The principal separates the students into at least two​ groups, one of which is the control group. This is essential to conducting a controlled experiment. D. This is an observational study. The principal does not assign a third party to identify the GPA of each student. Preventing bias so as to make the study​ double-blind is essential to conducting a controlled experiment.

b

The percentage of​ left-handed people in a certain country is estimated to be 9​%. Women are about six times as likely to be​ left-handed as men. Are gender and handedness independent or​ associated? Explain. Choose the correct answer below. A. Gender and handedness are independent because all of the possible combinations of each exist. B. Gender and handedness are associated because women are more likely to be​ left-handed than men. C. Gender and handedness are associated because the percentage is an estimate. D. Gender and handedness are independent because they are both comprised of mutually exclusive events.

b

What are the expected counts in a​ two-way table? Choose the correct answer below. A. The number of observations in each cell if the alternative hypothesis were true. B. The numbers of observations in each cell if the null hypothesis were true. C. The results of a survey. D. The probability of each event in the table.

b

What do large values of the​ chi-square statistic​ indicate? Choose the correct answer below. A. The null hypothesis cannot be rejected. B. One should be suspicious of the null hypothesis. C. The statistic was calculated incorrectly. D. The data conform to the null hypothesis.

b

What is one drawback with​ chi-square tests? Choose the correct answer below. A. The tests cannot reveal whether two variables are associated. B. The tests can reveal whether two variables are associated but not how they are associated. C. The tests are difficult to apply. D. The tests are difficult to apply and cannot reveal whether two variables are associated.

b

When events A and B are said to be​ independent, what does that​ mean? Choose the correct answer below. A. Events A and B are equally likely to occur. B. Knowledge that event B occurred does not change the probability of event A occurring. C. Events A and B are complements. D. Knowledge that event B occurred changes the probability of event A occurring.

b

A group of educators want to determine how effective tutoring is in raising​ students' grades in a math​ class, so they arrange free tutoring for those who want it. Then they compare final exam grades for the group that took advantage of the tutoring and the group that did not. Suppose the group participating in the tutoring tended to receive higher grades on the exam. Does that show that the tutoring​ worked? If​ not, explain why not and suggest a confounding variable. Choose the correct answer below. A. The study shows that the tutoring worked. B. Because this was an observational​ study, it only shows an​ association; it does not show that the tutoring worked. It could be that an insufficient number of students were studied to show that the tutoring worked. C. Because this was an observational​ study, it only shows an​ association; it does not show that the tutoring worked. It could be that more motivated students attended the tutoring and that was what caused the higher grades.

c

A study concludes that the use of pesticides is associated with the development of​ Parkinson's disease, a neurological disease that causes people to shake. The study reported that exposure to bug killers and weed killers is​ "associated with" an increase of​ 33% to​ 80% in the chances of getting​ Parkinson's. Does this study show that pesticides cause​ Parkinson's disease? Why or why​ not? Select the correct answer below. A. The study shows that pesticides cause​ Parkinson's disease. This was a controlled experiment because the only way to ensure exposure to pesticides is to use low levels of pesticides on the treatment group. Assuming all key features are​ satisfied, controlled experiments can conclude causation. B. The study shows that pesticides cause​ Parkinson's disease. In​ statistics, the term​ "associated with" is synonymous with​ "causes." Therefore, it may be concluded that pesticides cause​ Parkinson's disease. C. The study does not show that pesticides cause​ Parkinson's disease. This was an observational study because researchers could not have deliberately exposed people to pesticides. Observational studies cannot conclude causation. D. The study does not show that pesticides cause​ Parkinson's disease. The researchers did not administer a placebo along with the low levels of pesticides administered in the study.​ Therefore, a sufficiently robust control group was not established.

c

In​ 2008, a highway safety administration reported that the number of pedestrian fatalities in City A was 65 and that the number in City B was 45. Can we conclude that pedestrians are safer in City​ B? Why or why​ not? A. ​Yes, it can be concluded that pedestrians are safer in City B since 45 fatalities is less than 65 fatalities. B. ​No, City A may have more sidewalks and walkways for people to​ use, whereas City B may require walkers to use medians or shoulders causing them to be at a higher risk of an accident. C. ​No, in order to compare the fatalities the statistics must include the number of fatalities per pedestrian. There may be fewer pedestrians in City B causing the difference. D. ​No, although one city has a higher number of​ fatalities, pedestrians are in an equal amount of danger regardless of the city they are in.

c

Of the​ following, which is the only method of data collection suitable for making conclusions about causal​ relationships? Choose the correct answer below. A. Anecdotes B. Observational studies C. Controlled experiments D. All three are suitable.

c

One important use of the regression line is to do which of the​ following? Choose the correct answer below. A. To determine the strength of a linear association between two variables B. To determine if a distribution is unimodal or multimodal C. To make predictions about the values of y for a given​ x-value D. Both A and B are correct

c

The sample space of a random experiment with equally likely outcomes is​ what? Choose the correct answer below. A. Events that have no outcomes in common B. Any collection of outcomes of the experiment C. The set of all possible​ (and equally​ likely) outcomes of the experiment D. All possible combinations of outcomes of the experiment

c

The​ chi-squared statistic measures which of the​ following? Choose the correct answer below. A. The sum of all expected values for the cells of the​ two-way table. B. The product of the expected counts and the observed counts. C. The amount by which the expected counts differ from the observed counts. D. The amount of variability in the data set.

c

Which of the following is a reason we can never draw​ cause-and-effect conclusions from observational​ studies? Choose the correct answer below. A. Observational studies often do not involve a large enough sample to draw​ cause-and-effect conclusions. B. Observational studies are not scientific in nature. C. Potential confounding variables may explain the differences between groups rather than the treatment variable. D. Researchers may be biased in the observations they choose to record.

c

Answer the following questions about tests of proportions and​ chi-square tests. a. Are tests of proportions used for categorical or numerical​ data? b. Do​ chi-square tests apply to categorical or numerical​ data? a. Tests of proportions are used for ___________ data. b.​ Chi-square tests apply to _________ data.

categorical

Are hypothesis tests of proportions used for categorical or numerical​ data? Explain. A. Hypothesis tests of proportions are used for categorical data because proportions are numbers. B. Hypothesis tests of proportions are used for numerical data because proportions come from counts of categories. C. Hypothesis tests of proportions are used for numerical data because proportions are numbers. D. Hypothesis tests of proportions are used for categorical data because proportions come from counts of categories.

d

If events A and B are​ independent, what must be done to find the probability of event A AND​ B? Choose the correct answer below. A. Divide the probability of A and the probability of B. B. Add the probabilities of A and the probability of B. C. Subtract the probability of A and the probability of B. D. Multiply the probability of A and the probability of B.

d

In the special case in which both categorical variables have only two​ categories, the test of homogeneity is identical to which of the​ following? Choose the correct answer below. A. A​ two-tailed t-test of two means B. A​ one-tailed z-test of two proportions C. A​ one-tailed t-test of two means D. A​ two-tailed z-test of two proportions

d

Statistics and probability use the​ "inclusive OR". This means that referring to outcomes A OR B is referring to​ what? Choose the correct answer below. A. Outcomes that are only in A B. Outcomes that are in both A and B C. Outcomes that are only in B D. Outcomes that are only in​ A, only in​ B, or in both

d

Suppose a person is chosen at random. Use your knowledge about the world to decide whether the event that the person has blue eyes and the event that the person is female are independent or associated. Choose the correct answer below. A. The two events are associated because having blue eyes does not depend on being female. B. The two events are associated because being female depends on having blue eyes. C. The two events are independent because being female depends on having blue eyes. D. The two events are independent because having blue eyes does not depend on being female.

d

Under what conditions can extrapolation be used to make predictions beyond the range of the​ data? Choose the correct answer below. A. When the data set contains a large number of pairs of data. B. When there is a strong positive linear association in the data. C. When the correlation coefficient is close to −1 or +1. D. Never

d

What are controlled​ experiments? Choose the correct answer below. A. Experiments in which the results remain under the control of the researcher and are not shared for critique. B. Experiments in which all conditions are met for a​ chi-square test. C. Experiments in which subjects place themselves into treatment​ groups, by behavior or innate characteristics such as gender. D. Experiments in which the experimenters determine how subjects are assigned to treatment groups.

d

Fill in the blank. As the sample size is​ increased, the spread of the sample means​ _______.

decreases

When writing a regression​ equation, which of the following is not a name for the​ x-variable? Choose the correct answer below. Explanatory variable Predictor variable Independent variable Dependent variable

dependent variable

Fill in the blank below. The total area under a probability density curve​ _____.

equals 1

Attempting to use the regression equation to make predictions beyond the range of the data is called​ _______.

extrapolation.

The number of times a value is observed in a data set is called a​ ______.

frequency

Fill in the blank below. A hypothesis test to determine whether a distribution of categorical variables is following any proposed distribution is called​ a(n) ________ test.

goodness-of-fit

Fill in the blank below. For two or more samples and one categorical response​ variable, to determine if there is an association between categorical​ variables, a test of​ _________ is used.

homogeneity

Fill in the blank below. For one sample and two categorical response​ variables, to determine if there is an association between categorical​ variables, a test of​ _______ is used.

independence

The​ ___________ is found by adding all the data values and dividing by the total number of values.

mean

When an odd number of data values are arranged in​ order, the​ _________ is the middle value.

median

The value that divides a histogram into two equal areas is called the​ ____________. The value that serves as a balancing point for a histogram is the​ ____________.

median and mean

The data value that occurs with the greatest frequency is called the​ _______

mode

Fill in the blank. The spread of the distribution of the sample mean is​ _______ the spread of the population.

much smaller than

Are tests of means used for numerical or categorical​ data? Tests of means are used for _____ data.

numerical

Fill in the blank. ​Chi-square goodness-of-fit tests are applicable if the data consist of​ __________.

one categorical variable.

What is the term for a group of objects or people to be​ studied? Choose the correct answer below. Estimator Sample Census Population

population

The null hypothesis is always a statement about​ what? The null hypothesis is always a statement about a

population parameter

Fill in the blank below. The Normal model is a good​ first-choice to model data if the data are suspected to be​ _____.

symmetric and unimodal.

A data set on Shark Attacks Worldwide posted on StatCrunch records data on all shark attacks in recorded history including attacks before 1800. Variables contained in the data include time of​ attack, date,​ location, activity the victim was engaged in when​ attacked, whether or not the injury was​ fatal, and species of shark. Suppose a surfer wanted to learn if surfing during a certain time of day made one less likely to be attacked by a shark. Using the Shark Attacks Worldwide data​ set, which variables could the surfer use in order to answer this​ question? LOADING... Click the icon to view a subset of the data from Shark Attacks Worldwide. Select all that apply. - Location - Date - Time - Activity

time and activity

A large amount of scatter in a scatterplot is an indication that the association between the two variables is​ _______.

weak

Often, conditional probabilities are worded with what​ phrase? Choose the correct answer below. ​"given that" ​"mutually exclusive" ​"dependent" ​"either/or"

​"given that"

A student was wondering if students at her university arrived on campus each day the same way as another university. At the other​ university, 60%​ drove, 30% biked or​ walked, and the other​ 10% arrived using other means of transportation. The student randomly sampled 150 students one afternoon at her university and asked how they arrived at campus that day. Which hypothesis test should the student use to determine if students at her university arrive to campus in the same proportion as the other​ university? Choose the correct answer below. ​two-sample z-test for proportions ​Chi-square test of homogeneity ​one-sample z-test for proportions ​two-sample t-test ​Chi-square goodness of fit test

​Chi-square goodness of fit test