Chapter 8 Stats Honors

An SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. A 95% confidence interval for the difference pS - pH is

(-0.283, -0.038)

A researcher wants to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost, 12 of the 50 plants in group 1 exhibited damage and 18 of the 50 plants in group 2 showed damage. Let p1 be the actual proportion of all tomato plants of this variety that would experience damage under the kelp treatment, and let p2 be the actual proportion of all tomato plants of this variety that would experience damage under the no-kelp treatment. A 99% confidence interval for p1 - p2 is

(-0.354, 0.114)

In a large Midwestern university an SRS of 100 entering freshmen in 2014 found that 20 finished in the bottom third of their high school class. In 2016, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. In both years, the entering freshman class had roughly 6000 students. Let p1 be the proportion of all entering freshmen in 2014 who graduated in the bottom third of their high school class and let p2 be the proportion of all entering freshmen in 2016 who graduated in the bottom third of their high school class. Which of the following represents 99% confidence interval for p1 - p2?

(0.2 0.1) 2.576 square root 0.2(0.8)/100 + 0.1 (0.9)/ 100

A random sample of 900 individuals has been selected from a large population. It was found that 180 areregular users of vitamins. Thus, the proportion of the regular users of vitamins in the population is estimatedto be 0.20. What is the approximate value of the standard error of this estimate?

0.0133

A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and asked todetermine if the card featured one of five symbols: star, cross, circle, square, or three wavy lines. The psychicwas correct in 48 cases. If p represents the proportion of correct guesses the psychic made, what is thestandard error of p

0.0302

In an opinion poll, 25% of a random sample of 200 people said that they were strongly opposed to having astate lottery. What is the approximate standard error of the sample proportion?

0.0306

Eighty rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put througha simple maze. The maze required the rats to make a choice between going left or right at the outset. Sixty ofthe rats went right when running the maze for the first time. Assume that the eighty rats can be considered an SRS from the population of all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. What is the standard error for the proportion p of those who went right the first time when running the maze?

0.0484

An SRS of 50 students at a large middle school are asked, "Do you have a television in your bedroom?Twenty-eight of the students responded "yes." If p = the proportion of students who answered "yes," what isthe standard error of p?

0.070

A random sample of 200 female high school students in the United Kingdom showed that 110 are on Facebook. A separate random sample of 150 male high school students in the United Kingdom showed that 69 are on Facebook. Let p1 and p2 be the proportion of all female and male students in the U.K., respectively, who are on Facebook. Which of the following represents a 95% confidence interval for p1 - p2?

0.09+ square root 0.55(0.45)/200-0.46(0.54)/150

A sociologist is studying the effect of having children within the first two years of marriage on the divorcerate. Using hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. Which of the following gives the correct 90% confidence interval for the true proportion p of allcouples that had a child within the first two years of marriage and are divorced within five years?

0.40 ± 0.057

A newspaper conducted a statewide survey concerning the race for state senator. The newspaper selected arandom sample of 1200 registered voters and found that 620 of them plan to vote for the Republican candidate. Let p = the true proportion of all registered voters in the state that plan to vote for the Republican candidate. Which of the following gives the correct 90% confidence interval for p?

0.517 ± 0.024

After a college's football team once again lost a football game to the college's arch rival, the alumniassociation conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni fromthe population of all living alumni was selected. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p = the true proportion of all living alumni who favor firing the coach. Which of the following gives the correct 95% confidence interval for p?

0.64 ± 0.094

Researchers are studying the proportion of crops that are damaged at a large farm. The researchers plan toconstruct two 90% confidence intervals, each from a separate random sample, for the proportion of crops thatare damaged. Assuming the conditions for constructing the confidence intervals are met, what is theprobability that at least one of the constructed intervals will capture the true proportion of crops that are damaged?

0.99

A forester wants to produce a 90% confidence interval for the true proportion of hemlock trees in a forest that are infested with the Hemlock Woolly Adelgid, a serious insect pest. He needs the margin of error to be no more than 0.04. Which of the following equations can be used to find the smallest sample size that will produce such an interval?

1.64 square root (0.5)(0.5) divided by n <0.04

You are told that the proportion p of those who answered "yes" to a poll about internet use is p = 0.70, andthe standard error of the proportion is 0.0459. What was the sample size?

100

A marketing firm wants to estimate the true proportion of people in a city who use a certain brand of mobile phone. They want to produce a 90% confidence interval with a margin of error of at most 0.07. Which of the following is the smallest sample size that will produce the desired interval?

139

A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up on these couples, she finds that 80 couples are divorced within five years. Which of the following is closest to the sample size you would need to estimate p with a margin oferror of 0.02 with 90% confidence? Use p = 0.4 from the first sample as an approximation of p

1624

After a college's football team once again lost a football game to the college's arch rival, the alumniassociation conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni fromthe population of all living alumni was selected. Sixty-four of the alumni in the sample were in favor of firingthe coach. Let p = the true proportion of all living alumni who favor firing the coach. A 95% confidenceinterval for p is 0.64 ± 0.094. There are about 500,000 living alumni from this college. Based on these data we can be 95% confident thatthe true number of alumni that are in favor of firing the coach is captured in the interval from

273,000 to 367,000 alumni.

A newspaper conducted a statewide survey concerning the Pennsylvania state senator race. The newspaperselected a random sample of 1200 registered voters and found that 620 of them plan to vote for the Republican candidate. Let p = the true proportion of all registered voters in the state that plan to vote for the Republican candidate. A 90% confidence interval for p is 0.517 ± 0.024. There are about 8 million registered voters in Pennsylvania. Based upon these data we can be 90% confident that the true number of registered voters in Pennsylvania that plan to vote for the Republican candidate is

3.944 million to 4.328 million voters.

After a college's football team once again lost a football game to the college's arch rival, the alumniassociation conducted a survey to see if alumni were in favor of firing the coach. A random sample of 100alumni from the population of all living alumni was selected. Sixty-four of the alumni in the sample were infavor of firing the coach. Let p = the true proportion of all living alumni who favor firing the coach. Which ofthe following is closest to the sample size you would need to estimate p with a margin of error of 0.05 with95% confidence? Use p = 0.5 as an approximation of p.

385

In a random sample of 150 students on a large University campus of several thousand students, 90 studentsadmit to not getting enough physical activity (three or more days of vigorous exercise for at least 20 minutesor five or more days of moderate exercise for at least 30 minutes a week). A 90% confidence interval for p,the true proportion of all students at the University that do not get enough physical activity is 0.60 ± 0.066. There are 14,500 students that attend this University. Based upon these data we can be 90% confident thatthe true number of them that do not get enough physical activity is captured in the interval from

7,743 to 9,657 students.

A newspaper conducted a statewide survey concerning the 2008 race for state senator. The newspaperselected a random sample of 1200 registered voters and found that 620 would vote for the Republicancandidate. Let p = the true proportion of registered voters in the state that would vote for the Republicancandidate. Which of the following is closest to the sample size you would need in order to estimate p withmargin of error 0.01 with 95% confidence? Use p = 0.5 as an approximation of p

9604

A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time ittakes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds." Which of the following claims is justified?

A reporter claims that the mean amount of time it takes to apply the brakes after seeingthe brake lights on a vehicle in front of him is at least 1.2 seconds

A 95% confidence interval for p, the true proportion of all shoppers at a large grocery store who purchasecookies, was found to be (0.236, 0.282). Which of the following claims is justified

At least 23.6% of shoppers purchase cookies.

A political candidate is told by his polling organization that a 90% confidence interval for the true proportionof voters who support his candidacy is 0.45 to 0.53. Which of the following claims is justified?

At least 45% of registered voters favor this candidate.

Nine students from a random sample of 100 students at the University of Pittsburgh do not like to watch football. Five students from a random sample of 100 students at Penn State do not like to watch football. We would like to calculate a confidence interval for p1 - p2, the true difference in the proportion of students from each of these two universities that do not like to watch football. Which of the following conditions are met?

I and III

The college newspaper of a large Midwestern university periodically conducts a survey of students oncampus to determine the attitude on campus concerning issues of interest. Pictures of the studentsinterviewed along with quotes of their responses are printed in the paper. Students are interviewed by areporter "roaming" the campus selecting students to interview "haphazardly." On a particular day thereporter interviews five students and asks them if they feel there is adequate student parking on campus.Four of the students say, "no." Which of the following conditions for inference about a proportion using aconfidence interval are violated in this example? I. The data come from a random sample from the population of interest .II. The sample size is less than 10% of the population size. III. np 10 and n(1 - p) 10

I and III

Sixty-eight people from a random sample of 128 residents of Uppsala, Sweden, had blue eyes. Forty-five people from a random sample of 110 people from Preston, England, had blue eyes. We would like to calculate a confidence interval for p1 - p2, the true difference in the proportion of people from each of these two locations that have blue eyes. Which of the following conditions are met?

I, II, and III

A nationwide poll of 2,525 adults estimated with 95% confidence that the proportion of Americans who support health care reform is 0.78 0.0162. A member of Congress thinks that 95% confidence isn't enough.He wants to be 99% confident. How would the margin of error of a 99% confidence interval based on thesame sample compare with the 95% interval?

It would be larger, because higher confidence requires a larger margin of error.

A polling organization announces that the proportion of American voters who favor congressional term limitsis 64%, with a 95% confidence margin of error of 3%. Which of the following statements is a correctinterpretation of 95% confidence?

None of the above are correct.

A polling organization announces that the proportion of American voters who favor congressional term limitsis 64 percent, with 95% confidence and margin of error of 3 percent. This means that

None of the above are true.

There are 150 members at the First Baptist Church in Memphis, of which 145 say they pray regularly. There are 200 members at Faith Community Church in Nashville, of which 183 say they pray regularly. We would like to calculate a confidence interval for p1 - p2, the true difference in the proportion of members at each church that pray regularly. Which of the following conditions are met?

None of the conditions have been met.

A marketing company discovered the following problems with a recent poll: I. Some people refused to answer questions. II. People without telephones could not be in the sample. III. Some people never answered the phone in several calls. Which of these sources is included in the margin of error announced for the poll?

None of these sources of error.

A 95% confidence interval for the mean reading achievement score for a population of third-grade students is(44.2, 54.2). Suppose you compute a 99% confidence interval using the same data. Which of the following statements is correct?

The 99% confidence interval is wider.

A 95% confidence interval for p, the true proportion of all shoppers at a large grocery store who purchasecookies, was found to be (0.236, 0.282). Which of the following would be true about a 98% confidence interval constructed using the same data?

The interval would be wider, because the critical z* would be larger

The report of a sample survey of 1,014 adults says, "With 95% confidence, between 9% and 15% of allAmericans expect to spend more money on gifts this year than last year." What does the phrase "95% confidence" mean?

The method used to get the interval from 9% to 15%, when used over and over, producesintervals which include the true population percentage about 95% of the time.

A random sample of n1 female high school students in the United Kingdom showed that x1 are on Facebook. A separate random sample of n2 male high school students in the United Kingdom showed that x2 are on Facebook. Let p1 and p2 be the proportion of all female and male students in the U.K., respectively, who are on Facebook. Suppose the 95% confidence interval for the true difference in the proportion of females and males who are on Facebook is constructed. Which of the following is the best interpretation of the confidence interval?

We are 95% confident that the constructed interval captures the true difference in the proportion of female and male high school students in the U.K. who are on Facebook.

A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time ittakes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds." Which of the following statements correctly interprets this confidence interval

We are 95% confident that the interval from 1.2 to 1.8 seconds captures the true meanamount of time it takes for drivers to apply the brakes after seeing the brake lights on avehicle in front of him

A researcher wishes to see if a kelp extract helps prevent frost damage on tomato plants. One hundred tomato plants in individual containers are randomly assigned to two different groups. Plants in both groups are treated identically, except that the plants in group 1 are sprayed weekly with a kelp extract, while the plants in group 2 are not. After the first frost in the autumn, 8 of the 50 plants in group 1 exhibited damage, and 18 of the 50 plants in group 2 showed damage. Why would the use of z-procedures be questionable value in this situation?

We cannot be sure that the Normality condition has been met.

In a large Midwestern university an SRS of 100 entering freshmen in 2014 showed that 20 finished in the bottom third of their high school class. In 2016, an SRS of 100 entering freshmen showed that 10 finished in the bottom third of their high school class. In both years, the entering freshman class had roughly 6000 students. Which of the following best explains why it was important to know that the university had roughly 6000 entering freshman before using z-procedures in this situation?

We needed to know that the sample sizes were less than 10% of the population size.

Your teacher claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you've beenkeeping track. In the past 80 rolls, the number "five" has come up only 8 times. You suspect that thecalculator is producing fewer fives than it should. You would like to construct a 95% confidence interval forthe true proportion of fives generated by this calculator. Which of the following options gives the correctnotation for and value of the point estimate?

b. p(thingy on top)= 0.1

The Gallup Poll interviews 1600 people. Of these, 18% say that they jog regularly. The news report adds:"The poll had a margin of error of plus or minus three percentage points." You can safely conclude that

between 15% and 21% of people jog regularly

A 2008 Gallup poll found that 47% of Americans felt that a third political party is needed to represent theAmerican people. In the description of methods, the poll takers said: "For results based on the total sampleof national adults, one can say with 95% confidence that the maximum margin of sampling error is ±3percentage points." You can safely conclude that

between 44% and 50% of all Americans think we should have a third party.

Other things being equal, the margin of error of a confidence interval increases as the

confidence level increases.

A 2008 Gallup poll found that 47% of adults 18 years old or older in the United States felt that a thirdpolitical party is needed to represent the American people. In the description of methods, the poll takerssaid: "For results based on the total sample of U.S. adults, we can say with 95% confidence that the marginof error is ±3%." Among the poll respondents who identified their current party affiliation as "independent,"63% agreed that we need a third political party. The margin of error for those who identified with the"independent" party is

greater than ±3%, because only some of the people in the sample were independents, sothe sample size is smaller.

A 95% confidence interval for the mean of a population is computed from a random sample and found tobe 9 3.We may conclude that

if we selected many random samples and from each computed a 95% confidence intervalfor, approximately 95% of these intervals would contain u

A polling organization announces that the proportion of American voters who favor congressional term limitsis 64 percent, with a 95% confidence margin of error of 3 percent. If the opinion poll had announced themargin of error for 80% confidence rather than 95% confidence, this margin of error would be

less than 3%, because we require less confidence.

An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for theaverage yield for these plots is found to be 162.72 4.47 bushels per acre. Which of the following wouldproduce a confidence interval with a smaller margin of error than this one?

planting 100 plots, rather than 25

A 95% confidence interval for p, the true proportion of all shoppers at a large grocery store who purchasecookies, was found to be (0.236, 0.282). What are the values of the point estimate and margin of error forthis interval

point estimate = 0.259; margin of error = 0.023

A political candidate is told by his polling organization that a 90% confidence interval for the true proportionof voters who support his candidacy is 0.45 to 0.53. What are the values of the point estimate and margin oferror for this interval

point estimate = 0.49; margin of error = 0.04.

A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time ittakes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8seconds." What are the values of the point estimate and margin of error for this interval

point estimate = 1.5 seconds; margin of error = 0.3 seconds

We wish to construct a 99% confidence interval for the true mean oven temperature of a certain oven model.Four ovens of this model are selected at random. The dial on each is set to 300°F, and, after one hour, theactual temperature of each is measured. The temperatures measured are 305°, 310°, 300°, and 305°. Which ofthe following options gives the correct notation for and value of the point estimate

x 305

An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is 150bushels per acre. Assume that the yield per acre for the new variety of corn follows a Normal distributionwith unknown mean and that a 95% confidence interval for is found to be 150 ± 3.29. Which of thefollowing options gives the correct notation for and value of the point estimate?

x = 150