STATS QUIZZES

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Suppose you are going to roll a die 60 times and record , the proportion of times that a 1 or a 2 is showing. The sampling distribution of should be centered about

1/3

All but one of the following statements contain a blunder. Which one does not contain a blunder?

"The correlation between amount of fertilizer and yield of tomatoes was found to be r = 0.33."

In a particular game, a ball is randomly chosen from a box that contains three red balls, one green ball, and six blue balls. If a red ball is selected, you win $2, if a green ball is selected you win $4, and if a blue ball is selected you win nothing. Let x be the amount that you win. The expected value of x is

Incomes in a certain town are strongly right-skewed with mean $36,000 and standard deviation $7000. A random sample of 75 households is taken. What is the standard deviation of the sample mean?

$808.29

Drug sniffing dogs must be 95% accurate. A new dog is being tested and is right in 46 of 50 trials. Find a 95% confidence interval for the proportion of times the dog will be correct.

(0.805, 0.973)

A bank wants to get new customers for their credit card. They try two different approaches in their marketing campaign. The first promises a "cash back" reward; the second promises low interest rates. A sample of 500 people are mailed the first brochure; of these, 100 get the credit card. A separate sample of 500 people are mailed the second brochure; 125 get the credit card. Are the two campaigns equally attractive to customers? Compute a 95% confidence interval for the difference in the two proportions.

(-0.102, 0.002)

Your professor took a sample of the grade point averages for students in her class. For 25 students, the standard deviation of grade points was 0.65, and the mean was 2.89. A 95% confidence interval for the average grade point average for all students in her class is

(2.62, 3.16)

The gestation time of cats is approximately 68 days with a standard deviation of 3.9 days and is approximately Normally distributed. A sample of 35 kittens was selected. Assume that these are kittens that can be considered a random sample. What is a 90% confidence interval for the mean gestation time of kittens?

(66.92, 69.08)

A researcher wants to know if the average time in jail for robbery has increased from what it was several years ago when the average sentence was 7 years. He obtains data on 400 more recent robberies and finds an average time served of 7.5 years. If we assume the standard deviation is 3 years, a 95% confidence interval for the average time served is

(7.21, 7.79)

A student wanted to estimate the number of chocolate chips in a commercial brand of cookie. He sampled 100 cookies and found an average of 10.5 chips per cookie. If we assume the standard deviation is 8, what is a 99% confidence interval for the average number of chips per cookie?

(8.4, 12.6)

What is the impact of caffeine on performance in endurance cycling races? Thirty subjects were divided into 10 groups, and each group was given one of three doses of caffeine (0, 3, 6 mg/kg) in a drink, and the time to cycle the equivalent of 40 km on a stationary bicycle was recorded. Here is an (incomplete) diagram of the experiment.

(a) are subjects.

Is there a difference in the gestation time for first and second births to the same parent? The following table shows the gestation time (days) for a sample of four mothers with their first two children. Assume that the changes in gestation (second time - first time) have an approximately Normal distribution. A 90% confidence interval for the mean difference in gestation times between the first and second births is:

-2.5 ± 2.97

A machine fills cans of soda which are labeled "12 ounces," according to a Normal distribution with mean 12.1 ounces and standard deviation 0.1 ounces. If you buy a 12-pack of the soda, what is the chance the average contents of the cans will be less than advertised?

0.0003

0.0004

Sodas in a can are supposed to contain an average of 12 ounces. This particular brand has a standard deviation of 0.1 ounces, with an average of 12.1 ounces. If the can's contents follow a Normal distribution, what is the probability that the mean contents of a six pack are less than 12 ounces?

0.007

A salesman makes visits to customers. Based on his past history, the probability he makes a sale on any visit is 0.15. It is reasonable to assume that customers' decisions are independent of one another. If he makes 10 visits in a day, what is the chance he makes at least five sales?

0.0099

A noted psychic was tested for ESP. The psychic was presented with 400 cards face down and asked to determine if each card was marked with one of four symbols: a star, cross, circle, or square. The psychic was correct in 120 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. Suppose you wish to see if there is evidence that the psychic was doing better than just guessing. To do this you test the hypothesesH0: p = 0.25,Ha: p > 0.25.The P-value of your test is

0.0104

What is the P-value for a test of the hypotheses H0: μ = 10 against Ha: μ ≠ 10 if the calculated statistic is z = 2.56?

0.0104

What proportion p of adults received a parking ticket in the last year? In a survey of 400 adults selected using random digit dialing, 40 received a parking ticket in the last year. The standard error for the proportion of adults receiving a parking ticket is

0.015

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent. The standard error for a confidence interval for the candidate's latest support level is

0.016

The SAT scores of entering freshmen at University X have a N (1200, 90) distribution and the SAT scores of entering freshmen at University Y have a N (1215,110) distribution. A random sample of 100 freshmen is sampled from each University, with the sample mean of the 100 scores from University X and the sample mean of the 100 scores from University Y. The probability that is greater than , the population mean for University Y, is

0.0475

A sociologist is studying the effect of a college degree on the divorce rate five years after being married. She selects a random sample of 220 couples who both have college degrees, 97 of which were divorced within five years. Of 180 couples where at least one of the couple did not have a college degree, 92 were divorced. Let p1 be the proportion who were divorced within five years for the couples where both had a college degree, and p2 is the proportion who were divorced within five years of the other group. The estimate of p2 - p1 is

0.0702

A sociologist is studying the effect of a college degree on the divorce rate 5 years after being married. She selects a random sample of 220 couples who both have college degrees, 97 of whom were divorced within five years. Of 180 couples where at least one of the couple did not have a college degree, 92 were divorced. Let p1 be the proportion who were divorced within five years for the couples where both had a college degree, and p2 is the proportion who were divorced within five years of the other group. A 90% confidence interval for p2 - p1 is

0.0702 ± 0.0824

An SRS of 100 of a certain popular model car in 1993 found that 20 had a certain minor defect in the brakes. An SRS of 400 of this model car in 1994 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1993 and 1994, respectively, that actually contain the defect. A 90% confidence interval for p1 - p2 is

0.075 ± 0.071

Suppose that scores on the Math SAT exam follow a Normal distribution with mean 500 and standard deviation 100. Two students that have taken the exam are selected at random. What is the probability that the sum of their scores exceeds 1200?

0.0793

A forced-choice design is often used to compare the attractiveness of pheromones to insects. A Y-tube is used. The pheromone is placed on one branch, the control on the second branch, and the insect on the third branch. The insect then chooses one of the two branches. Suppose that 45 of 75 insects choose the pheromone branch. What is the P-value for the hypothesis test of no preference?

0.083

A sample of 75 students found that 55 of them had cell phones. The margin of error for a 95% confidence interval estimate for the proportion of all students with cell phones is

0.100

There are 20 multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points, and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. If the student needs at least 40 points to pass the test, the probability the student passes is closest to

0.1019

Incomes in a certain town are strongly right-skewed with mean $36,000 and standard deviation $7000. A random sample of 75 households is taken. What is the probability the sample mean is greater than $37,000?

0.1075

The 200 students in a statistics class were randomly divided into two groups of 100 students. Both groups were given the same midterm exam at the same time. One group took the exam in a classroom in which the air temperature was normal (68º). The other group was given the exam in a similar room in which the air temperature was unusually warm (84º). Both groups had one hour to complete the exam. Seventy-four of those taking the exam in the normal room passed, while only 66 of those taking the exam in the warm room passed. Let p1 and p2 represent the probability of passing under normal and warm conditions, respectively. To determine if this is evidence that students perform worse under uncomfortable conditions, you test H0: p1 = p2, Ha: p1 > p2. The P-value of this test is

0.1093

A multiple choice test has four possible answers for each question. Let X be the number of correct responses in a test of 100 questions if the student simply guesses on each question. Let X be the number of correct guesses by your friend in the 100 trials. What is the probability that X ≥ 30 if your friend is just guessing? Use the Normal approximation with the continuity correction.

0.1492

A researcher wanted to know if the content of television programs has an impact on viewers' recall of ad content. He randomly assigned 108 people to view a program with violent content and 110 people to view a program with neutral content. The same nine commercials were inserted into each program. After viewing the program, the subjects were asked to recall the brands advertised in the commercials. The average number of brands recalled for those who saw the violent program was 3.77 with standard deviation 1.87. The average number of brands recalled for those who saw the neutral program was 4.65 with standard deviation 1.67. The standard error for is

0.240

Suppose that you are a student worker in the Statistics Department and agree to be paid by the Random Pay system. Each week the Chair flips a coin. If the coin comes up heads, your pay for the week is $80; if it comes up tails, your pay for the week is $40. You work for the department for 100 weeks (at which point you have learned enough probability to know the system is not to your advantage). The probability that , your average earnings in the first two weeks, is greater than $65 is

0.2500

Suppose that about 20% of students in school have used marijuana in the last year. In order to preserve anonymity during surveys, a technique called randomized response is often used. A student is approached and asked to flip a coin but not show it to the interviewer. If the coin is heads, the student answers the question: "Was your mother born in January to June (inclusive)?" If the coin is tails, the student answers the question: "Have you used marijuana in the last year?" Because the interviewer does not know the outcome of the coin flip, the students' responses are confidential. What is the probability then that if a yes is received, the student used marijuana in the last year?

0.29

A random variable X has a density curve shown in the graph below.

0.3

Let the random variable x be a random number with the uniform density curve given below. P (0.7 < x < 1.1) has value

0.30

Should a student union at a college open a pub? About 20% of the student body is in favor of this issue. Suppose that five students are surveyed.What is the probability that no students in your (small) survey will be in favor of opening a pub?

0.3277

Lactose intolerance causes difficulty digesting dairy products that contain lactose (milk sugar). It is particularly common among people of African or Asian ancestry. At a college, 70% of the population is white; 20% is black; and 10% is Asian. Moreover, 15% of whites, 70% of blacks, and 90% of Asians are lactose intolerant. Consider the (partially) completed tree diagram below:

0.335

The time for students to complete a standardized placement exam given to college freshman has a normal distribution with a mean of 62 minutes and a standard deviation of 8 minutes. If students are given one hour to complete the exam, the proportion of students who will complete the exam is about:

0.40

Parking on campus is often expensive, and it is tempting to park illegally and take your chances on getting a ticket. From past experience, the probability of getting a ticket is about 0.30 on any given day, and because you always change your parking location, each day's outcome is independent of the previous day's outcome.The probability that you will NOT get a ticket on two days is

0.49

From a sample of 400 births, the standard deviation of the gestation time was 10 days and the mean was 250 days. The standard error for the sample was

0.5

A bank is investigating ways to entice customers to charge more on their credit cards. (Banks earn a fee from the merchant on each purchase, and they hope to collect interest from the customers, as well). A bank selects a random group of customers who are told their "cash back" will increase from 1% to 2% for all charges above a certain dollar amount each month. Of the 500 customers who were told the increase applied to charges above $1000 each month, the average increase in spending was $527 with standard deviation $225. Of the 500 customers who were told the increase applied to charges above $2000 each month, the average increase in spending was $439 with standard deviation $189. When testing whether or not the increases in spending are different, the test is significant at

0.5%

Most people think babies are equally likely to come as either a boy or a girl. This is not true. Actually, about 51.3% of all babies are boys. If a family has two children (not twins), what is the chance they have one boy and one girl?

0.50

People with type O-negative blood are universal donors. That is, any patient can receive a transfusion of O-negative blood. Only 7.2% of the American population have O-negative blood. If 10 people appear at random to give blood, what is the probability that at least one of them is a universal donor?

0.53

In a small town, 60% of the households have a pet dog. If a household has a pet dog, there is a 70% chance that the household also owns a cat. If a household does not have a dog, there is a 30% chance that the household owns a cat. What is the probability that a randomly selected household owns a cat?

0.54

Ten-year-old children from two populations in a polluted city are tested. The first group was of children born in 1990, and the second was of children born in 1995. An SRS of 400 ten-year-old children born in 1990 showed that 20 children had respiration disorders. An SRS of 100 ten-year-old children born in 1995 showed that ten children had respiration disorders. Let p1 and p2 be the proportions of all ten-year-old children born in that city in 1990 and 1995, respectively, that have respiration disorders. Is there evidence of a difference in the proportion of children having respiration disorders among the two populations? To make this determination, you test the hypotheses and . The P-value of your test is

0.602

Walleye is a common game fish. Adult walleye have a length with a mean of 44 cm and a standard deviation of 4 cm, and the distribution of lengths is approximately Normal. What fraction of walleye are between 40 and 48 cm in length?

0.68

Females in a certain class rated their intelligence with a mean of 6.5. The males in the same class rated their intelligence with a mean of 7.25. The difference in the mean ratings (male -female) was

0.75

0.77

One hundred rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats to make a choice between going left or going right at the outset. Eighty of the rats went right when running the maze for the first time. Assume that the 100 rats can be considered an SRS from the population of all rats born to mothers exposed to high levels of tobacco smoke during pregnancy (note that this assumption may or may not be reasonable, but researchers often assume lab rats are representative of large populations since they are often bred to have uniform characteristics). Let p be the proportion of rats in this population that would go right when running the maze for the first time. A 90% confidence interval for p is

0.8 ± 0.066

Suppose X is a continuous random variable taking values between 0 and 1 and having a probability distribution described by the following density curve.

0.875

As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.200. Different shoppers can be regarded as independent trials. If is the proportion of the next 100 shoppers that buy a packet of the crackers after tasting a free sample, then the probability that fewer than 30% buy a packet after tasting a free sample is approximately (don't use the continuity correction)

0.9938

The weight of medium-sized oranges selected at random from a large bin of oranges at the local supermarket is a random variable with mean µ = 12 ounces and standard deviation = 1.2 ounces. The weight of the oranges, in pounds (1 pound = 16 ounces) is a random variable with standard deviation

0/075 pounds

A pediatrician is interested in studying the effect of Motrin on reducing temperature in young children. Four children with influenza have their temperatures taken immediately before and then 45 minutes after taking a standard dose of Motrin with the following results:A 95% confidence interval for the average reduction in temperature from using Motrin is

1.275 ± 1.793.

The weight of a medium size orange selected at random from a large bin of oranges at the local supermarket is a random variable with mean μ = 12 ounces and standard deviation σ = 1.2 ounces. Suppose we independently pick two oranges at random from the bin. The expected value of the sum of the weights of the two oranges, in pounds (1 pound = 16 ounces) is

1.5

A local farmer is interested in comparing the yields of two varieties of tomatoes. In an experimental field, he selects 20 locations and assigns 10 plants from each variety at random to the locations. He determines the yield per plant (in pounds). The mean yield for plants of variety 1 was = 16.3 pounds with a standard deviation s1 = 3 pounds. The mean yield for plants of variety 2 was =18.4 pounds with a standard deviation s2 = 4 pounds. The standard error of the difference in sample means is

1.58 pounds

You want to construct a 92% confidence interval. The correct z* to use is

1.75

Females in a certain class rated their intelligence with a mean of 6.5 with standard deviation 1.12. The males in the same class rated their intelligence with a mean of 7.25, with standard deviation 1.50. The standard deviation of the difference in the ratings (male - female) was

1.87

A fair coin is tossed, and a fair six-sided die is rolled. Suppose the outcomes for the coin and die are independent. The probability of getting a head and rolling a 6 is

1/12

A random variable has the density curve as in the graph below.

1/2

A refrigerator contains 6 apples, 5 oranges, 10 bananas, 3 pears, 7 peaches, 11 plums, and 2 mangos. Imagine you stick your hand into the refrigerator and pull out a piece of fruit at random. What is the probability you pick a plum?

1/4

A national poll of 600 men announced that the proportion in the survey who claimed to help their wives at home was 85%. If we took a larger poll of 1200 men, about how many would we expect to say that they help their wives at home, based on the first survey?

1020

A researcher wanted to know if the content of television programs has an impact on viewers' recall of ad content. He randomly assigned 108 people to view a program with violent content, and 110 people to view a program with neutral content. The same nine commercials were inserted into each program. After viewing the program, the subjects were asked to recall the brands advertised in the commercials. The average number of brands recalled for those who saw the violent program was 3.77 with standard deviation 1.87. The average number of brands recalled for those who saw the neutral program was 4.65 with standard deviation 1.67. The conservative degrees of freedom for the t distribution are

107

As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.200. Different shoppers can be regarded as independent trials. Let be the proportion of the next n shoppers that buy a packet of the crackers after tasting a free sample. How large should n be so that the standard deviation of is no more than 0.01?

1600

The most common intelligence quotient (IQ) scale is Normally distributed with mean 100 and standard deviation 15. Many school districts across the country seek to identify "Gifted and Talented" children for special enrichment programs. Typically, these children must have IQ scores in the top 5%. What is the minimum score to qualify a child for these programs?

125

The population of men with a localized prostate tumor and a certain pretreatment has been studied. It was found that the probability of 5-year survival is equal to 0.8. The mean number of patients among 20 patients with a localized prostate tumor and a pretreatment that survive 5 years is

How well does a new medication reduce blood pressure relative to baseline? The reduction in blood pressure for these patients follows an approximate normal distribution with unknown mean µ and standard deviation σ = 10 mm Hg. How many patients need to be measured to estimate the mean change in blood pressure to within 2 mm Hg at the 99% confidence level?

166

From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the probability that more than 68% will favor the incumbent?

17.1%

In an experiment on a new drug, subjects were randomly assigned to either a placebo or the active drug. In addition, the method of delivery of the drug (pill, skin patch, or nasal mist) was considered. In this experiment, there were how many factors?

Consider the following plot with three different lines drawn. What is the slope of the line labeled (b)?

A researcher wanted to know if the content of television programs has an impact on viewers' recall of ad content. He randomly assigned 18 people to view a program with violent content, and 20 people to view a program with neutral content. The same nine commercials were inserted into each program. After viewing the program, the subjects were asked to recall the brands advertised in the commercials. The average number of brands recalled for those who saw the violent program was 3.77 with standard deviation 1.87. The average number of brands recalled for those who saw the neutral program was 4.65 with standard deviation 1.67. The t* multiplier for a 95% confidence interval using the conservative degrees of freedom is

2.110

The value of t* for a 95% confidence interval when there were 15 pieces of data is

2.145

From March 1981 to February 1983, the number of burglaries committed each month in a Georgia town were recorded. They are given in the accompanying chart. Between months 12 and 13, a law was enacted requiring citizens to own a gun. Town officials felt this law might decrease the number of burglaries by acting to deter criminals.

2.83

A biology class has 201 students. The five-number summary for the midterm exam was 23, 51, 62, 78, 92. The student with the 92 found a grading error on her exam, and her correct grade was 95. There were no other grading errors. After correcting this student's paper, the five-number summary for the midterm exam will be:

23, 51, 62, 78, 95

26.3%

The gestation time for humans is approximately to be Normally distributed with mean μ. The average gestation time of a random sample of 25 babies is found to be = 245 days, and the standard deviation of the 25 gestation times is found to be s = 10 days. A 90% confidence interval for μ is

245 ± 3.42

There are 20 multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is worth 5 points and only one response per question is correct. Suppose a student guesses the answer to each question, and her guesses from question to question are independent. The student's mean score on the exam should be

A sample of 160 workers in the downtown area classified each worker by race. A bar graph of the results is given below, but the bar for black workers in the graph below has been omitted.

25%

How long is your morning commute? The following are times (minutes) of your morning commute during the first two weeks of the fall term. 43 62 49 47 98 53 55 48 42 47. The variance of morning commute is:

269.4 minutes2.

To assess the accuracy of a kitchen scale, a standard weight known to weigh 1 gram is weighed a total of n times and the mean, , of the weighings is computed. Suppose the scale readings are Normally distributed with unknown mean, µ, and standard deviation σ = 0.01 g. How large should n be so that a 90% confidence interval for µ has a margin of error of ± 0.0001?

27061

A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. In a pilot study of a random sample of 100 blooms, 77 yield marketable strawberries. What sample size should be used for a future study to ensure that the margin of error is less than 5 percentage points, 95% of the time?

273

A researcher believes that there is a linear relationship between BMI (kg/m2) of pregnant mothers and the birth weight (BW in kg) of their newborn. The regression line for the data the researcher provides is . The predicted BW for BMI = 45 kg/m2 is

3.252 kg

Suppose we have a loaded die which gives the outcomes 1 through 6 according to the probability distributionNote that for this die all outcomes are not equally likely as they would be if this were a fair die. If this die is rolled 6000 times, then , the sample mean of the number of spots on the 6000 rolls, should be about

3.30

How well does a new medication reduce blood pressure relative to baseline? One hundred patients had their blood pressure measured before and after taking the drug. The average reduction in blood pressure for these patients is = 30 mm Hg. Assume that the reduction in blood pressure for the new medication follows a normal distribution with unknown mean µ and standard deviation σ = 10 mm Hg. A 90% confidence interval for µ is

30 ± 1.645

Suppose we have a loaded die which gives the outcomes 1 through 6 according to the following probability distribution.Note that for this die all outcomes are not equally likely as they would be if this were a fair die.If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about

3000

High levels of glucose in the blood are indicative of diabetes, which is becoming more prevalent in the United States. Diabetes can lead to many complications such as blindness and heart disease. A random sample of 180 individuals had their blood sugar level measured. The results are displayed in the graph.

33%

Students at University X must be in one of the class ranks, Freshman, Sophomore, Junior, or Senior. At University X, 35% of the students are Freshmen and 30% are Sophomores. If a student is selected at random, the probability he or she is either a Junior or a Senior is

35%

The gestation time of humans has an approximate Normal distribution with a mean of 250 days and a standard deviation of 6.0 days. A simple random sample of newborns is taken. How large of a sample is needed so that the sampling distribution of has a standard deviation of 1 day?

Consider the following stemplot. The mean of the data represented in this stemplot is

A sportswriter wishes to see if a football filled with helium travels farther, on average, than a football filled with air. To test this theory, the writer uses 18 adult male subjects, randomly divided into two groups of 9 subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean yardage for group 1 was 1 = 30 yards, with a standard deviation s1 = 8 yards. The mean yardage for group 2 was 2 = 26 yards, with a standard deviation s2 = 6 yards. Assume the two groups of kicks are independent. Let µ1 and µ2 represent the mean yardage observed for the entire population if all members of the population kicked, respectively, a helium- and air-filled football. Assuming two-sample t procedures are safe to use, a 90% confidence interval for µ1 - µ2 is (use the conservative value for the degrees of freedom)

4 ± 6.2 yards.

Researchers compared two groups of competitive rowers: a group of skilled rowers and a group of novices. The researchers measured the angular velocity of each subject's right knee, which describes the rate at which the knee joint opens as the legs push the body back on the sliding seat. The sample size n, the sample means, and the sample standard deviations for the two groups are given below.The researchers wished to test the hypotheses

4.00

4.33

An SRS of 20 third grade children is selected in Chicago and each is given a test to measure their reading ability. We are interested in a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. The margin of error associated with the confidence interval is

4.64 points

A dataset consists of the composition of 77 breakfast cereals. For each cereal, the number of calories/serving and the grams of fat/serving were measured. A regression line was obtained as follows:Calories = 110 + 10 (grams of fat)Suppose that two cereals differ by 5 grams of fat per serving. The caloric content per serving would differ by

50 calories

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent. We want to know if his support has decreased. In computing a test of hypothesis with , what is the estimate of the overall proportion, ?

51.5%

The lifetime of a 2-volt nonrechargeable battery in constant use has a Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than

541.60 hours

Foresters use regression to predict the volume of timber in a tree using easily measured quantities such as diameter. Let y be the volume of timber in cubic feet and x be the diameter in feet (measured at 3 feet above ground level). One set of data givesy = -30 + 60xThe predicted volume for a tree of 18 inches is

60 cubic feet

A survey was conducted of students asking about their usage of marijuana in the last year (Never, Occasional, Regular) and the amount of alcohol and/or marijuana usage by their parents (Neither, One, Both). Here is a table of data.The conditional probability that the parents use one of alcohol or marijuana given a student never used marijuana is

68/226 = 0.30 = 30%

In a controversial election district, 73% of registered voters are Democrat. A random survey of 500 voters had 68% Democrats. Are the bold numbers parameters or statistics?

73% is a parameter, and 68% is a statistic.

The scores on the Survey of Study Habits and Attitudes (SSHA) for a sample of 150 first-year college women produced the following boxplot and descriptive statistics using MINITAB.

The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the top 10% of students are given A's, what is the lowest mark that a student can have and still be awarded an A?

76.08

It has been asserted that 15% of all people are left-handed. In a random group of 10 people, what is the chance that not all of them are right-handed?

80.3%

You wish to find a 95% confidence interval for the mean number of times men change channels with a remote control during a commercial. Based on a preliminary study, you estimate σ = 15. How many commercials' worth of data do you need to have a margin of error no more than 3?

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60 high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be = 6 hours with a standard deviation s1 = 3 hours. The researcher also obtained an independent SRS of 40 high school students in a large, city school district and found the mean time spent in extracurricular activities per week to be = 4 hours with a standard deviation s2 = 2 hours. Let and represent the mean amount of time spent in extracurricular activities per week by the populations of all high school students in the suburban and city school districts, respectively. If the researcher used the more accurate software approximation to the degrees of freedom, he would have used which of the following for the number of degrees of freedom for the two-sample t procedures?

A survey interviews 1000 Americans by telephone and asks "What do you think is the biggest problem facing education today?" The population of interest for this poll is most likely

American adults

You have computed a 95% confidence interval for the mean, μ, of a population as (13, 20). Based on this interval, you can say

Both choices are correct.

You want to know which of two manufacturing methods will be better. You create ten prototypes using the first process, and ten using the second. There were three defectives in the first batch and five in the second. The 90% confidence interval for the difference in the two proportions is (-0.493, 0.159). What conclusion should you make about the two manufacturing processes?

Both methods are equivalent.

Which of the following events are disjoint?

Choose a student at random from a statistics class. Event A is that the student is a Junior. Event B is that the student is a Senior.

Ginger root is used by many as a dietary supplement. A manufacturer of supplements produces capsules that are advertised to contain at least 500 mg of ground ginger root. A consumer advocacy group doubts this claim and tests the hypotheses H0: = 500 Ha: < 500 based on measuring the amount of ginger root in a SRS of 100 capsules. Suppose the results of the test fail to reject H0 when, in fact, the alternative hypothesis is true. In this case, the consumer advocacy group will have

Committed a Type II error.

We perform a statistical test to examine if the mean amount filled of soft drinks has increased when cans are filled by a new machine compared to the old machine. Which of the following is a Type II error?

Conclude that the new machine did not increase the mean amount filled when in fact it does.

Conclude that the new machine increased the mean amount filled when in fact it does not.

It has been claimed that women live longer than men; however, men tend to be older than their wives. Ages of sixteen husbands and their wives from England were obtained. The null hypothesis of equality of means is rejected. What conclusion can be made from this study?

English husbands are older than their wives.

A researcher wants to know if tougher sentencing laws have had the desired impact in terms of deterring crime. He plans to select a sample of states which have enacted a "3 strikes" law and compare violent crime rates before the law was enacted with crime rates two years later. The correct set of hypotheses to test are

Explanation: This is correct. If the laws have deterred crime, the crime rates will have gone down, and the mean crime rate should be less after the new laws than before.

Suppose there is a deck of three cards, one marked with a 1, one marked with a 2, and one marked with a 5. You draw two cards at random and without replacement from the deck of three cards. The sample space s = {(1, 2), (1, 5), (2, 5)} consists of these three equally likely outcomes. Let x be the total of the two cards drawn. Which of the following is the correct set of probabilities for x?

Explanation: This is the correct answer. If the (1, 2) is drawn, then the sum is a 3; if the (1, 5) is drawn the sum is a 6; and if the (2, 5) is drawn the sum is a 7. Each of the three possible pairs is equally likely, so the three sums are equally likely as well and each must have probability 1/3.

Here is a list of employees at a small firm that have been "numbered" for convenience. The following is part of a random number table. 16124 45998 60679 05487 98825 29942 13522 01868 85705 12053The third employee chosen will be:

Gupta

The manager of an automobile dealership is considering a new bonus plan to increase sales. Currently, the mean sales rate per salesperson is 5 automobiles per month. The correct set of hypotheses to test the effect of the bonus plan is

H0: μ = 5, Ha: μ > 5

Twelve people who suffer from chronic fatigue syndrome volunteer to take part in an experiment to see if shark fin extract will increase one's energy level. Eight of the volunteers are men, and four are women. Half of the volunteers are to be given shark fin extract twice a day and the other half a placebo twice a day. We wish to make sure that four men and two women are assigned to each of the treatments, so we decide to use a block design with the men forming one block and the women the other. The names of the men and women are given in the chart and each name is given a numerical label.Use the list of random digits below to assign four men and two women to the shark fin treatment. Read the table from left to right, first selecting the four men and then the two women. Use the numerical labels given in the chart to the names.The people assigned to the shark fin treatment are

Lewis, Simpson, Howard, Adams, Braun, Miller.

Some researchers were asked to recheck the statistics on a paper they were writing about the impacts of a group of new science courses. They had performed 63 statistical tests on their data at α = 5% and had found four "significant" results. They were excited. Should they have been?

Maybe. It depends on the actual results.

As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is 0.200. Different shoppers can be regarded as independent trials. If is the proportion of the next 100 shoppers that buy a packet of the crackers after tasting a free sample, then has approximately a

N (0.2, 0.04) distribution.

Suppose that you are a student worker in the Statistics Department and agree to be paid by the Random Pay system. Each week the Chair flips a coin. If the coin comes up heads, your pay for the week is $80; if it comes up tails, your pay for the week is $40. You work for the department for 100 weeks (at which point you have learned enough probability to know the system is not to your advantage). Suppose is your average pay for the 100 weeks. Then, has approximately a

N (60, 2) distribution.

A college basketball player makes 80% of his free throws. At the beginning of a game he misses his first two free throws. We may correctly conclude

Neither answer is correct

A random sample of 85 students in Chicago city high schools take a course designed to improve SAT scores. Based on these students, a 90% confidence interval for the mean improvement in SAT scores for all Chicago city high school students is computed as (72.3, 91.4) points. The correct interpretation of this interval is

Neither choice is correct.

For each of the 50 states and Washington, D.C., a number of statistics related to education are available for 1992. Among these are the average salary of all high school teachers and the percentage of high school seniors who took the SAT exam. The following is a scatterplot of the average teacher salary and the percentage of students taking the SAT exam for all 50 states and Washington, D.C. in 1992.

Neither choice is correct.

Experiments on learning in animals sometimes measure how long a laboratory rat takes to find its way through a maze. Suppose for one particular maze, the mean time is known to be 20 seconds with a standard deviation of σ = 2 seconds. Suppose also that times for laboratory rats are Normally distributed. A researcher decides to test whether rats exposed to cigarette smoke take longer on average to complete the maze. She exposes 25 rats to cigarette smoke for 15 minutes and then records how long each takes to complete the maze. The mean time for these rats is 20.6 seconds. Are these results significant at the α = 0.05 level? Assume the researcher's rats can be considered an SRS from the population of all laboratory rats.

On a certain airline, the chance the early flight from Atlanta to Chicago is full is 0.8. The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Are the two flights being full independent events?

On a certain airline, the chance the early flight from Atlanta to Chicago is full is 0.8. The chance the late flight is full is 0.7. The chance both flights are full is 0.6. Can we believe the two flights being full are independent events?

A physical therapist studying muscular strength is willing to assume muscle strength scores are Normally distributed with a standard deviation 18 and mean 85. A sample of 10 individuals demonstrates a mean muscular strength score of 85.1. Is there significant evidence that μ > 85? Give the P-value for the test.

P-value = 0.4928. The data do not give significant evidence that μ > 85.

A survey was conducted to investigate views on gun control. One thousand homes in a county were phoned, but responses were only obtained from 200 households. Two different questions were asked on alternate households:(a) Should more controls be placed on gun ownership to prevent random gun violence by unstable people?(b) Should less controls be placed on gun ownership to help people defend themselves from violent crime.Which of the following is correct?

People often have strong opinions on gun control. This could lead to response bias.

A recent study investigated the extent to which hypertension is affected by alcohol consumption. Among other things, the study compared the rate of hypertension in nondrinkers to the rate in people that are moderate beer drinkers (average between 0.5 and 1 glass of beer per day). They found that a 95% confidence interval for the relative risk of hypertension in moderate beer drinkers as compared to nondrinkers was 0.47 to 0.90. A relative risk of 1 means that the two groups have the same risk of hypertension, while a relative risk of less than 1 means that moderate beer drinkers have less risk of hypertension than nondrinkers. If the researchers who ran the study had tested the hypotheses H0: the relative risk for moderate beer drinkers as compared to nondrinkers = 1Ha: the relative risk for moderate beer drinkers as compared to nondrinkers ≠ 1 they would have concluded which of the following?

Reject H0 at level 0.10

Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women aged 20 to 34 vary approximately Normally with mean 185 milligrams per deciliter (mg/dl) and standard deviation 39 mg/dl. Cholesterol levels for middle-aged men vary Normally with mean 222 mg/dl and standard deviation 37 mg/dl. Sandy is a young woman with a cholesterol level of 220. Her father has a cholesterol level of 250. Who has relatively higher cholesterol?

Sandy

Subjects should read the Web for information about the study.

Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Here is the output from a regression analysis:

The about 84% of the variation in the number of larvae is explained by changes in the number of stumps

Which of the following does not have an error?

The correlation between students' IQ scores and their foot size is 0.67.

Consider the following plots of the correlation between two variables:

The correlation in (a) is about 0.5

A recent article in an educational research journal reports a correlation of +0.8 between math achievement and overall math aptitude. It also reports a correlation of -0.8 between math achievement and a math anxiety test. Which of the following interpretations is the most correct?

The correlation of +0.8 is just as strong as the correlation of -0.8.

Which tutorial method is more effective in learning calculus? Two tutorial sections of a calculus course were created where one section has graduate student tutors and the other section had faculty tutors. Students were free to sign up for either tutorial section. The final grades of the students were compared at the end of the course. Which of the following is correct?

The explanatory variable is the type of tutor.

Which of the following is correct?

The matched pairs t test is the same as the one-sample t test but done on the differences.

The following is a plot of the number of alligator bites over time in Florida.

The maximum number of bites recorded over this period is about 25 per year.

A sample of breakfast cereals was classified as either a hot or cold cereal. In addition, the number of calories/serving and grams of fat/serving (integer values) were measured. It was also recorded whether each cereal meets the daily nutritional requirements for iron, using the following scale: 0 = does not meet daily nutritional requirements for iron; 1 = meets not more than 25% of daily nutritional requirements for iron; 2 = meets more than 25% of daily nutritional requirements for iron. Which of the following is correct?

The number of calories/serving is a quantitative variable

For the density curve displayed below, which of the following is true?

The proportion of outcomes exceeding 1.5 is equal to 0.25

Which of the following is correct?

The t procedures can be used with an SRS of more than 40 observations even if the data are skewed.

The Multiple Listing Service (MLS) provides many pieces of information about homes for sale, such as area of the lot (square feet), living area (square feet), if house has a view (yes/no), and the number of stories (1, 1 ½, 2). Which of the following is correct?

The variable "number of stories" is categorical

The world record time (in minutes) in the marathon is plotted versus the year in which the record was set for men and women separately. The plotting symbol o is used for men and x for women. The data include only records set between 1908 and 1988.

The world record times for women show a greater rate of improvement (decrease more rapidly) than the world record times for men.

The following is a plot of the number of alligator bites over time in Florida.

There are about 3x more bites in the 1990s than in the 1970s.

Which of the following statements is consistent with the scatterplot?

There is an outlier in the plot and, if the least-squares line were fit to the data, it would have a negative residual.

Suppose that the random variable X has a distribution with a density curve that looks like the following:

This is correct. By the central limit theorem, the sampling distribution of the sample mean of 100 observations should be approximately normal.

A plumbing contractor puts in bids on two large jobs. Let the event that the contractor wins the first contract be A and the event that the contractor wins the second contract be B. Which of the following Venn diagrams has shaded the event that the contractor wins exactly one of the contracts?

This is correct. The detailed explanation is included in the Venn diagram below. It is the union of the event "gets A but not B" and "gets B but not A."

A random sample is collected of size n from a population with standard deviation σ and with the data collected a 95% confidence interval is computed for the mean of the population. Which of the following would produce a new confidence interval with smaller width (smaller margin of error) based on these same data?

Use a smaller confidence level

For a physics course containing 11 students, the maximum point total for the quarter was 200. The point totals for the 11 students are given in the stemplot below.

We can compute the mean number of points for the 11 students from the information in the stemplot.

Ginger root is used by many as a dietary supplement. A manufacturer of supplements produces capsules that are advertised to contain at least 500 mg of ground ginger root. A consumer advocacy group doubts this claim and tests the hypothesesH0 μ: = 500 Ha: μ < 500They take a random sample of 100 ginger root capsules produced by the manufacturer and compute the test statisticwhere is the mean amount of ginger root in the 100 capsules sampled. Based on other information, the advocacy group knows the value of α. If the test statistic z has value 2.39, we may conclude that

We do not reject H0 at level α = 0.05.

A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output.

We don't have enough information to conclude whether or not the regression is useful.

A statistics instructor wants to know which route will get her to school the fastest. Each day from October 2 to November 15, when she gets to the turn point she checks the odometer on her car. If it shows an even number she takes the freeway; if it shows an odd number, she takes the in-town route. She records the total time each day. At the end of the study, if she detects a significant difference in time, can she conclude it is due to the route?

Yes

Does the value of the standard deviation depend on the value of the mean?

Yes. You need to know the mean to be able to calculate the standard deviation

You are thinking of using a t procedure to construct a 95% confidence interval for the mean of a population. You suspect the distribution of the population is not Normal and may be skewed. Which of the following statements is correct?

You may use the t procedure provided your sample size is large, say at least 50.

There are four people in a familya father, a mother and two childrenand they have won two tickets to go to Disneyland for a week. They decide to select a sample of two people for the trip as follows: The mother and father flip a coin to see which of the two of them will go, and they then flip a coin to see which of the two children will go. This is

a probability sample from the family since each member of the family has a known chance of being selected to go on the trip.

A researcher is interested in the cholesterol levels of adults in the city in which she lives. A cholesterol screening program is set up in the downtown area during the lunch hour. Individuals can walk in and have their cholesterol determined for free. The service is used by 173 people, and their average cholesterol is 217.8. The sample obtained is an example of

a sample probably containing bias and undercoverage

A researcher is interested in the cholesterol levels of adults in the city she lives in. A free cholesterol screening program is set up in the downtown area during the lunch hour. Individuals can walk in and have their cholesterol determined for free. One hundred and seventy-three people use the service and their average cholesterol is 217.8. The sample obtained is an example of

a sample probably containing bias and undercoverage.

A small college has 500 Freshmen, 400 Sophomores, 350 Juniors, and 300 Seniors. Administrators wish to conduct a survey of their students and find a simple random sample of 50 Freshmen, 40 Sophomores, 35 Juniors, and 30 Seniors. The overall sample is

a stratified sample

Below is a plot of the Olympic gold medal winning performance in the high jump (in inches) for the years 1900 to 1996. From this plot, the correlation between the winning height and year of the jump is

about 0.95

A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by the dealer from which they bought their car. A simple random sample of 1000 Canadians found that 58% were satisfied with the service provided by the dealer from which they bought their car. The sampling variability associated with these statistics is

about the same

In order to assess the opinion of students at the University of Montana on campus snow removal, a reporter for the student newspaper interviews the first 12 students he meets who are willing to express their opinion. In this case, the population is

all students at the University of Montana

A teacher gave a 25-question multiple choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this information

all the students had the same score.

In the graph below, the circled point is

an influential point. Deleting it should increase the estimate of the slope.

You want to conduct a poll to discover the proportion of individuals who believe that global warming is not going to be a problem. If you believe the proportion is about 80%, how many individuals will you need to sample to have a 90% confidence interval with a margin of error no more than 5%?

at least 174

The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a Normal distribution with mean that varies slightly from year to year and standard deviation 6.0. You plan to take an SRS of size n of the students who took the ACT exam this year and compute the mean score of the students in your sample. You will use this to estimate the mean score of all students this year. In order for the standard deviation of to be no more than 0.1, how large should n be?

at least 300

A sample was taken of the salaries of 20 employees from a large company. The following are the salaries (in thousands of dollars) for this year (the data are ordered). 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77. Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The interquartile range of the salaries will

be unchanged

Ten years ago a study at a large midwestern university found that 18% of the students at the university were very optimistic about their prospects of finding a satisfying job after graduation. To determine if opinions have changed, an SRS of 100 students currently enrolled at the university was selected. Twenty-five percent of those selected were optimistic about their prospects of finding a satisfying job after graduation. Let p be the proportion of the current student population that is optimistic about their prospects of finding a satisfying job after graduation. The P-value of a test of H0: p = 0.18, Ha: p ≠ 0.18 is

between 0.05 and 0.10.

A study sponsored by American Express Co. and the French government tourist office found that old American stereotypes about French unfriendliness weren't true. The respondents were more than 1000 Americans who have visited France more than once for pleasure over the past two years. The results of this study are probably

biased, overstating the extent to which the old stereotypes weren't true.

A researcher is studying the effects of a new drug on reducing high blood pressure. He recruits 250 men to test the new active drug against a current standard. At the end of six weeks, the decrease in systolic blood pressure will be evaluated. He believes the drug will be more effective for black men than for white men. To properly test his belief, the experiment should be

blocked

Two amateur gardeners are interested in comparing the yields of two varieties of tomatoes. They each have small backyard gardens. Each gardener is going to plant three plants of each variety in his garden. The first gardener will select six small areas in his garden for planting, then choose three of these at random for the three plants of the first variety and then use the remaining three for the second variety. The second gardener will follow the same procedure with his own randomization in his garden. At the end of the growing season they will compare the yields of the two varieties. In this example the gardens are

blocks

An eager statistics student wanted to help his boss. He studied the data on products sold at the store over a period of a week and reported to his boss that the average UPC number was 1001264789 with a standard deviation of 45378. From this information his boss should

do nothing with the information. The statistics reported are invalid.

A drug manufacturer is studying how a new drug behaves in patients. Investigators compare two doses, 5 milligrams (mg) and 10 mg. The drug can be administered by injection, skin patch, or intravenous drip. Concentration in the blood after 30 minutes is then measured. The factor(s) in this study are

drug dose and how it's administered

The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Northside High, 36 seniors take the test. If the scores at this school have the same distribution as national scores, the sampling distribution of the average (sample mean) score for the 36 students is

exactly Normal

experiement

Suppose that the population of the scores of all high school seniors that took the SAT-V (SAT verbal) test this year follows a normal distribution with mean µ = 480 and standard deviation σ = 90. A report claims that 10,000 students who took part in a national program for improving one's SAT-V score had significantly better scores (at the 0.05 level of significance) than the population as a whole. In order to determine if the improvement is of practical significance one should

find out the actual mean score of the 10,000 students.

A survey of 1000 adults ages 30 to 35 is conducted. The number of years of schooling and the annual salary for each person in the survey is recorded. The correlation between years of schooling and annual salary is found to be 0.27. Suppose instead the average salary of all individuals in the survey with the same number of years of schooling was calculated and the correlation between these averages and years of schooling was computed. This correlation would most likely be

larger than 0.27

23. A student has obtained the following computer output from a regression examining the relationship between BTU input to a furnace and the BTU output.

for every BTU input to a furnace, the output increases by 0.911, on average.

Suppose that you are a student worker in the Statistics Department, and they agree to pay you using the Random Pay system. Each week the Chair flips a coin. If it comes up heads, your pay for the week is $80, and if it comes up tails, your pay for the week is $40. You work for the department for two weeks. Let be the average of the pay you receive for the first and second week. The sampling distribution of is

given by the following probability distribution. Probability: 0.25 0.50 0.25

I want to examine the relationship between the number of calories/serving and the grams of fat/serving in breakfast cereals. The explanatory and response variables are

grams of fat/serving; calories/serving.

In the race for mayor of Columbus, Ohio, in 1999, one poll found that 61.1% of those surveyed would vote for the Democratic candidate. The poll had a 4.1% margin of error with 95% confidence. We may correctly conclude that

if the poll were repeated many times and a 95% confidence interval computed for each, approximately 95% of these would include the true percentage of the population that would vote for the Democratic candidate.

A social psychologist reports that "in our sample, ethnocentrism was significantly higher (P < 0.05) among church attendees than among nonattendees." This means

if there is actually no difference in ethnocentrism between church attendees and nonattendees, the chance that we would observe a difference as large or larger than we did is less than 5%.

Suppose we toss a penny and a nickel. Let A be the event that the penny is a head and B be the event that the nickel is a tail. The events A and B are

independent

Ann Landers once asked her female readers whether they would be content with affectionate treatment from men, with no sex ever. Over 90,000 women wrote in, with 72% answering "Yes." Why shouldn't we believe the results of this "poll?"

it was a voluntary response

A researcher wants to study the effect of regular exercise on cholesterol levels. The researcher compares the cholesterol levels of 50 people who belong to a local gym and exercise regularly with the cholesterol levels of 50 people from the community who did not exercise regularly. The cholesterol levels of the members of the gym were substantially lower. The researcher can conclude that

members of a local gym who exercised regularly had lower cholesterol levels than those in the community who did not exercise regularly.

There are two statistics classes. The first has 250 students, and the second has 200 students. In the first class, the students are instructed to toss a coin 20 times and record the value of , the proportion of heads. The instructor then makes a histogram of the 250 values of obtained. In the second class, the students are instructed to toss a coin 40 times and record the value of , the proportion of heads. The instructor then makes a histogram of the 200 values of obtained. The histogram of values for the first class should be

more variable since it is based on a smaller number of tosses.

You receive a fax with six bids (in millions of dollars)2.2, 1.3, 1.9, 1.2, 2.4, and x,where x is some number that is too blurry to read. Without knowing what x is, the median

must be between 1.3 and 2.2

A noted psychic was tested for ESP. The psychic was presented with 400 cards face down and asked to determine if each card was matched with one of four symbols: a star, cross, circle, or square. The psychic was correct in 120 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. How large a sample n would you need to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.25 as the value for p.

n = 7203

As the degrees of freedom become larger, the difference between the t and z distributions becomes

narrower

A researcher examines data from all cities with populations over 100,000 in the United States. He notices that those cities that have a major league baseball team tend to have a greater number of divorces than other cities. One can reasonably conclude that

neither choice is correct

Below is a plot of the Olympic gold medal winning performance in the high jump (in inches) for the years 1900 to 1996. The equation of the least-squares regression line of Winning Height (in inches) on Year isWinning Height = -364.90 + 0.23 YearIn another millennium (the year 3000), if the Olympics continue to be held, we can expect the Winning Height to be about

neither choice is correct

The accompanying two histograms represent the distribution of acceptance rates (percent accepted) among 25 business schools in 1995. The histograms use different class intervals, but are based on the same data. In each class interval, the left endpoint is included but not the right.Which statement is true?

neither choice is correct

It has been claimed that women live longer than men; however, men tend to be older than their wives. Ages of 16 husbands and their wives from England were obtained. These data should be analyzed with a

paired samples t test.

A researcher measures a response variable Y and explanatory variable X on each of several objects. A scatterplot of the measurements is as follows:

r is meaningless here.

Consider a study performed by a medical center to determine which of two heart surgeries is most effective: angioplasty (running plastic tubes through the arteries) or bypass (rerouting arteries). The purpose of either procedure is to prolong the life of the patient. The study records the survival time of each patient (measured from the time of the surgery). The response and explanatory variables in this study are:

response variable: survival time; explanatory variable: type of surgery.

s = {apple, orange, banana, pear, peach, plum, mango}

A game consists of drawing three cards at random from a deck of playing cards. You win $3 for each red card that is drawn. It costs $2 to play. For one play of this game, the sample space s for the net amount you win (after deducting the cost of play) is

s= {-$2, $1, $4, $7}

A major study examined the relationship between cause of death (heart attack, cancer, stroke, accident, etc.) and age. A good way to graphically represent the relationship is with

side-by-side boxplots

I want to examine whether there is a relationship between a student's grade point average and after-college plans. For a visual display of the data I should choose

side-by-side boxplots

A researcher reports that a test is "significant at 5%." This test will be

significant at 10%.

A distribution has a mean of 100 and a median of 120. The shape of this distribution is most likely

skewed left

The scores of individual students on the American College Testing (ACT) Program College Entrance Exam have a normal distribution with mean 18.6 and standard deviation 6.0. At Westside High, 400 students take the test. Assume their scores are all independent. If the scores at this school have the same distribution as nationally, the probability that the average of the scores of all 400 students exceeds 19.0 is

smaller than the probability that a single student has a score exceeding 19.0

Based on surveys conducted in 1989 and 1999, a researcher compared the proportion of high school age females interested in a career in science in 1989 with the proportion in 1999. He concluded that the proportions were not significantly different at the = 0.05 level because the P-value was 0.121. Assuming the surveys were simple random samples from the appropriate populations, we may conclude

that the probability of observing a difference at least as large as that observed by the researcher if, in fact, the two proportions were equal is 0.121.

A sociologist wants to study the attitudes of American male college students toward marriage and husband-wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. The sample in this situation is

the 25 men who received and returned the questionnaire.

Which of the following measures are not affected by outliers?

the IQR

The ABC Company has been evaluating the performance of two advertising agencies with which it deals. They produce the following scatterplot of sales against advertising expenditures. The two agencies are indicated on the plot with different symbols. From the plot, the ABC Company should decide

the Omega Company is better than Alpha¯sales are generally higher even with less expenditure on advertising

Suppose we are testing the null hypothesis H0: µ = 50 and the alternative Ha: µ ≠ 50 for a normal population with σ = 6. The 95% confidence interval for the mean is (51.3, 54.7). Then

the P-value for the test is less than 0.05.

A local farmer is interested in comparing the yields of two varieties of tomatoes. In an experimental field, she selects 40 locations and assigns 20 plants from each variety at random to the locations. She determines the average per plant (in pounds). She computes a 95% confidence interval for the difference in mean yields between the two varieties using the two-sample t procedures with the resulting interval (2.13, 6.41). For testing using the two-sample t procedures we can say that

the P-value must be less than 0.05.

Consider the plot of the number of drownings in a state vs. the total ice cream sales for the state over a 15-year period.

the average temperature during the summer.

The sampling distribution of a statistic is

the distribution of values of the statistic over repeated samples from the population.

Sampling variability refers to

the idea that different samples will give different statistics.

A business has two types of employees: managers and workers. Managers earn either $100,000 or $200,000 per year. Workers earn either $10,000 or $20,000 per year. The number of male and female managers at each salary level and the number of male and female workers at each salary level are given in the two tables below.

the mean salary of female managers is $40,000 greater than that of male managers.

In a class of 25 students, 22 students had grades between 71 and 80 (both endpoints included), and three students had grades between 91 and 100 (both endpoints included). For these data,

the median must be between 71 and 80

A student computed a 95% confidence interval for the mean, μ, of a population as (13, 20). Based on this interval,

the method gives correct results 95% of the time.

the probability of concluding that the new machine increased the mean amount filled when in fact it does

Suppose the average Math SAT score for all students taking the exam this year is 480 with standard deviation 100. Assume the distribution of scores is normal. A SRS of four students is selected and given special training to prepare for the Math SAT. The mean Math SAT score of these students is found to be 560, 80 points higher than the national average. We may correctly conclude

the results are neither statistically significant at level α = 0.05 nor practically significant.

A statistics instructor wants to know which route will get her to school the fastest. Each day from October 2 to November 15, when she gets to the turn point she checks the odometer on her car. If it shows an even number, she takes the freeway; if it shows an odd number, she takes the in-town route. She records the total time each day. What is the explanatory variable in this study?

the route

Students often incorrectly believe that inference for a population proportion based on the sample proportion is always valid if n > 30. They are confusing a general rule of thumb for the central limit theorem which says that as the sample size, n, gets large becomes Normally distributed with a different rule for proportions. The correct rule for proportions is that we can create confidence intervals for p based on if

there are at least 15 successes and 15 failures. This is correct.

The five-number summary of scores on a test is 35 60 65 70 90 Based on this information

there are both high and low outliers.

The data in the scatterplot below are an individual's weight and the time it takes (in seconds) on a treadmill to raise his or her pulse rate to 140 beats per minute. The o's correspond to females and the +'s to males.

there is a negative correlation between time and weight for males and for females.

A sociologist is studying the effect on the divorce rate of having children within the first three years of marriage. From city marriage records she selects a random sample of 400 couples who were married for the first time between 1985 and 1990, with both members of the couple between 20 and 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples who had children, 83 were divorced within 5 years, while in the couples who didn't have children within three years only 52 were divorced. Suppose p1 is the proportion of couples married in this time-frame who had a child within the first three years and were divorced within five years, and p2 is the proportion of couples married in this time-frame who did not have a child within the first three years and were divorced within five years. The sociologist hypothesized that having children early would increase the divorce rate. She tested the one-sided alternative and obtained a P-value of 0.0314. The correct conclusion is that

there is evidence of an association between divorce rate and having children early in a marriage.

For small samples, t intervals are ___________ z intervals based on the same data set.

wider than

z = -1.3991

A poll finds that 54% of the 600 people polled favor the incumbent. Shortly after the poll is taken, it is disclosed that he had an extramarital affair. A new poll finds that 50% of the 1030 polled now favor the incumbent. We want to know if his support has decreased. The test statistic is

z = 1.56

Blood samples taken from children up to ten years old in a certain town show that 54% of the 600 tested have blood-type O. Twenty years later, a new set of blood samples from children up to 10 years old finds that 50% of the 1030 tested now have blood-type O. We want to know if between the first and second tests there was a decrease in the proportion of children having blood type O. The test statistic is

z = 1.56

From previous polls, it is believed that 66% of likely voters prefer the incumbent. A new poll of 500 likely voters will be conducted. In the new poll, if the proportion favoring the incumbent has not changed, what is the mean and standard deviation of the number preferring the incumbent?

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