EBook Problems GLM Predict

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EBook Problems Set - Variation and Prediction Intervals

Problem 1

Two researchers are going to take a sample of data from the same population of physics students. Researcher A will select a random sample of students from among all students taking physics. Researcher B's sample will consist only of the students in her class. Both researchers will construct a 95% confidence interval for the mean score on the physics final exam using their own sample data. Which researcher's method has a 95% chance of capturing the true mean of the population of all students taking physics?

  • Choose one answer.
(a) Research B
(b) Researcher A
(c) Both methods have a 95% chance of capturing the true mean
(d) Neither
Answer


Problem 2

A random sample of 150 UCLA students found that 35% of the respondants wanted a elevator to replace Bruin Walk. A 95% confidence interval for the percentage of all UCLA students who feel this way is approximately:

  • Choose one answer.
(a) (24%, 46%)
(b) (32%, 38%)
(c) The sample size is too small to compute a confidence interval.
(d) (27%, 43%)
Answer


Problem 3

According to Terry Prachett, the short unit of time in the multiverse is the New York second, defined as the time interval between the light turning green and the cab behind you honking. A magazine took a poll of 100 New Yorkers and found that 90 people agree with that statement wholeheartedly. Which of the following is a 90% confidence interval for the proportion of people who agree with that statement?

  • Choose one answer.
(a) 0.9 +\- 0.50
(b) 0.9 +\- .05
(c) 0.9 +\- .03
(d) 0.9 +\- .06
Answer


Problem 4

A national poll found that 62% of all Americans agreed that more attention should be paid to mental health of war veterans. If a simple random sample of 326 people was used to make a 95% confidence interval of (0.57,0.67), what is the margin of error?

  • Choose one answer.
(a) 0.03
(b) 0.05
(c) 0.12
(d) In order to calculate the margin of error, we need the p-value of the population.
Answer


Problem 5

Hermione Granger is on a mission this year to complain about the astronomical cost of wizarding books to the Hogwart board of administrators. Given that the population mean for book cost is 10 and a standard deviation of 2 galleons, If Hermione were to take a simple random sample of 49 students and make a 68% confidence interval, what would be the range of values for the sample mean or Xbar?

  • Choose one answer.
(a) 8 and 12 galleons
(b) 9.4 and 10.6 galleons
(c) 6 and 14 Galleons
(d) 9.7 and 10.3 galleons
Answer


Problem 6

A 95% confidence interval indicates that:

  • Choose one answer:
(a) 95% of the intervals constructed using this process based on samples from this population will include the population mean
(b) 95% of the time the interval will include the sample mean
(c) 95% of the possible population means will be included by the interval
(d) 95% of the possible sample means will be included by the interval
Answer


Problem 7

Suppose we want to find out if a coin is not fair. To test this hypothesis we flip the coin 100 times, and in 63 out of 100 flips we get heads. We construct the confidence interval and find it to be (.53,.73). Interpret this confidence interval.

  • Choose one answer.
(a) 95 is the Z score that corresponds to our distribution of sample means
(b) Confidence is something you learn at fraternity parties
(c) 95% of the time the true proportion of flips that are heads is between .53 and .73
(d) If we were to repeat this experiment over and over again, 95 times out of 100 our Confidence interval would cover the true proportion of flips that are heads
Answer


Problem 8

A 95% confidence interval is calculated for a sample of weights of 100 randomly selected pigs, and is (42 pounds, 48 pounds). Will the sample mean weight fall within the confidence interval?

  • Choose one answer.
(a) Yes
(b) We need more information to determine if this is true.
(c) No
Answer


Problem 9

The average number of fruit candies in a large bag is estimated. The 95% confidence interval is (40, 48). Based on this information, you know that the best estimate of the population mean is:

  • Choose one answer.
(a) 43
(b) 40
(c) 45
(d) none of the above.
(e) 44
Answer


Problem 10

Suppose we plan to take a random sample of adults in the U.S. and determine the percent of them who have attended church in the last 30 days. We calculate a 90% confidence interval for the proportion of all adults in the U.S. who attended church in the last 30 days. Which of the following changes in our plans would result in a wider confidence interval?

  • Check all that apply.
(a) Using an 85% confidence level.
(b) Using a 95% confidence level.
(c) Using a larger sample.
(d) Using a smaller sample.
Answer


Problem 11

Kevin has always, ever since he was a wee lad, wondered what proportion of the candies in M&M chocolate candies bags are yellow. However, his persistent calls to the M&M headquarter were of no avail. Now that he wields the awesome power of being a TA for Stat 10, he makes each of his 200 students go buy a M&M bag, count the colors, and compute a 99% confidence intervals for the yellow candy proportion. Assume that each M&M bag is a random sample, approximately how many of the 200 confidence intervals will not capture the true population proportion for yellow M&M's?

  • Choose one answer.
(a) Not enough information for an answer
(b) 0 to 4
(c) 4 to 8
(d) 12 to 14
(e) 8 to 12
Answer


Problem 12

A 95% confidence interval for the proportion of U.S. adults who favor the death penalty is given by (0.03, 0.09). Is the following statement true or false?

"There is a 95% probability that an adult in the US is in favor of the death penalty."

(a) True
(b) False
Answer


Problem 13

Suppose that one day, after a refreshing work out at the gym, you want to know how many of the people in the North campus know who John Wooden is. You walk into the deep North, carefully avoiding the people holding skulls and muttering in Elizabethan english. Once you are at the center of North campus, you nicely ask the North campus majors to stop chasing butterflies and then took a random sample of 100 students. 30 say that they know who John Wooden is.

What is the 95% confidence interval for the true percentage of North campus majors who know about John Wooden?

  • Choose one answer.
(a) 29.5 to 30.5%
(b) 29.95 to 30.05%
(c) 20.8 to 39.2%
(d) 25.4 to 34.9%
Answer


Problem 14

The church of Pastafarian wants to know how many people in a city of 1 million would like to attend its church services. After sending out volunteers to do a simple random sample, the church finds a 90% confidence interval. Which of the following should have been done to make the confidence interval smaller?

  • Choose one answer.
(a) Not enough information to tell
(b) Increasing the sample size
(c) Decreasing the sample size
(d) Use a 68% confidence interval instead
Answer


Problem 15

A few years after the events of 'The Jedi Returns', Luke Skywalker, as the new Jedi Master, is thinking of establishing a Jedi church on his home world of Tatooine. He would like to know what proportion of people would be interested in coming to church, so he uses his Jedi Mind powers to select a simple random sample of 1000 people, and then read their minds to see whether they would are interested in a Jedi church.

He computes a 95% confidence interval. What could he have done in order to increase the decrease the length of the confidence interval? Check all that applies

  • Choose at least one answer.
(a) Decrease the sample size
(b) Increase the sample size
(c) Use a 68% confidence interval instead
(d) Use a 99% confidence interval instead
Answer


Problem 16

A college instructor wants to be 99% certain of the mean math anxiety score for freshman enrolled in college algebra. What is the best way for him to do this?

  • Choose one answer.
(a) Test on mean against a hypothesized constant.
(b) Test the difference between the two means of independent samples.
(c) Use a chi-squared test of association.
(d) test for a difference in more than two means (one way ANOVA).
(e) Test the difference in means between two paired or dependent samples.
(f) Test that a correlation coefficient is not equal to 0 (correlation analysis).
(g) Construct a 99% confidence interval.
Answer


Problem 17

At the magical Unseen University, many freshman have very inadequate background in mathematics. Professor Rincewind wants to contruct a 95% confidence interval for the proportion of freshman who has inadequate background in mathematics. What is the best way?

  • Choose one answer.
(a) Test one mean against a hypothesized constant.
(b) Test that a correlation coefficient is not equal to 0 (correlation analysis).
(c) Test the difference between the two means of independent samples.
(d) Construct a 99% confidence interval.
(e) Construct a 95% confidence interval.
Answer


Problem 18

We observe the math self-esteem scores from a random sample of 25 female students. How should we determine the probable values of the population mean score for this group?

  • Choose one answer.
(a) test that a correlation coefficient is not equal to 0 (correlation analysis).
(b) Test one mean against a hypothesized constant.
(c) Test the difference between two means (independent samples).
(d) Use a chi-squared test of association.
(e) Test for a difference in more than two means (one way ANOVA).
(f) Test the difference in means between two paired or dependent samples.
(g) Construct a confidence interval.
Answer


Problem 19

Sauron the Dark Lord of Mordor, taking a break from looking for his Ring of Power, engages in a little statistical exploration. His orc soldiers, though a perennial favorite as henchmen and soldier for many of the most popular Dark Lords, frequently suffer from low self esteem. Sauron wants to initiate a self-esteem enhancement program called "You're beautiful, it's true", but first he wants to know the probable population average self-esteem score. He takes a sample of the self-esteem score of 49 orc soldiers. What is the best way to calculate the probable average self esteem score?

  • Choose one answer.
(a) Test that a correlation coefficient is not equal to 0 (correlation analysis).
(b) Construct a confidence interval.
(c) test the difference in means between two paired or dependent samples.
(d) Test for a difference in more than two means (one way ANOVA).
(e) Use a chi-squared test of association.
(f) Test one mean against a hypothesized constant.
(g) Test the difference between two means (independent samples).
Answer


Problem 20

Which of the following values will always be within the upper and lower limits of a confidence interval for mean?

  • Choose one answer.
(a) The sample size.
(b) The sample mean.
(c) The population mean.
(d) The standard deviation of the sample.
Answer


Problem 21

Tiffany Aching, the most famous witch in all of the Chalk, has recently learned about confidence interval from a wandering stat teacher (she paid him an egg for 1 hour's worth of lesson). To practice, she computes the 95% confidence interval for the mean weight of pigs from a simple random sample of 49 pigs. How many times will the true population mean fall within the confidence interval?

  • Choose one answer.
(a) Most of the time.
(b) All the time, because the calculation of the confidence interval requires the true population mean.
(c) Not enough information to tell.
(d) None of the time.
Answer


Problem 22

Imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. The researchers are trying to estimate the mean hours of sleep that freshmen get at night. Each researcher takes a random sample of size 50 from the same population of freshmen, and constructs a 95% confidence interval for the mean. Approximately how many of these 100 confidence intervals will not capture the true mean?

  • Choose one answer.
(a) 95 to 100.
(b) Other.
(c) None.
(d) 3 to 7.
(e) 1 or 2.
(f) About half.
Answer


Problem 23

A particular psychological test is used to measure academic motivation. The average test score for all university students nationwide is 115. A university estimates the mean test score for students in its economic major by testing a random sample of n students and constructing a confidence interval based on their scores. Which of the following statements about the confidence interval are true?

I. The resulting interval will contain 115 II. The 95 percent confidence interval for n = 100 will generally be more narrow than the 95 percent confidence interval for n = 50. III. For n = 100, the 95 percent confidence interval will be wider than the 90 percent confidence interval.

  • Choose one answer.
(a) I only
(b) II only
(c) II and III
(d) III only
Answer


Problem 24

Saruman the White, after seeing the vast success Sauron had in improving the self-esteem of his orc henchmen, decided to initiate a similar program with his orc soldiers. But first, Saruman wanted to estimate the average self-esteem score of his orcs in Isengard. The true population average for self esteem score is 20. Saruman estimates that average by taking a sample of n orcs and then constructing a confidence interval.

What of the following is true?

I. The resulting interval will contain 20 II. The 95 percent confidence interval for n = 100 will generally be more narrow than the 95 percent confidence interval for n = 50. III. For n = 100, the 95 percent confidence interval will be wider than the 90 percent confidence interval.

  • Choose one answer.
(a) II only
(b) III only
(c) I only
(d) II and III
Answer


Problem 25

A simple random sample of 400 graduate students at American universities is taken. Of these students, 72% were born in the United States and 28% were born in other countries. A 90% confidence interval for the percentage of all graduate students at American universities who were born in other countries is

  • Choose one answer.
(a) 28% +/- 0.50%.
(b) 28% +/- 1.31%.
(c) 28% +/- 3.39%.
(d) 28% +/- 3.70%.
Answer


Problem 26

Professor Severus Snape has given Harry Potter detention again. To keep Harry Potter occupied, Professor Snape assigned Harry the task of estimating the proportion of Muggle-born students ( student wizards who were born to parents who are BOTH Muggle) within Hogwarts School of Magic.

Harry dutily took a simple random sample of 225 students. Of these students, 30% are Moogle-born, and 70% are not. The 90 % confidence interval for the percentage of Muggle-born students is

  • Choose one answer.
(a) 0.3 +/- 0.031
(b) 0.3 +/- 0.46
(c) 0.3 +/- 0.075
(d) 0.3 +/- 0.090
Answer


Problem 27

A poll at the magical Unseen University showed that 75% of the wizard students would like to have an elevator installed in the Unseen Tower- the tallest building in the whole campus. These students complain that having to levitate themself 300 feet every single day to get to class is too tiring, and that usually leaves them too tired to party at night. The other 25%, mostly wizards nerds, do not favor installing an elevator.

What is the 95% confidence interval for the proportion of student wizards who favor installing an elevator?

  • Choose one answer.
(a) Not enough information for an answer
(b) 0.75 +/- 0.09
(c) 0.75 +/- 0.43
(d) 0.75 +/- 0.04
Answer


Problem 28

We want to estimate the percentage of people who order popcorn at the movies. Out of a random sample of 400 people who watched movies at a local theatre, 120 mention that they order popcorn. What is the 99% confidence interval?

  • Choose one answer.
(a) (120/400) +/- 1.96 * SE(p hat)
(b) (120/400) +/- 1.96 * SE(P)
(c) (120/400) +/- 2.57 * SE(p hat)
(d) (120/400) +/- 2.57 * SE(P)
Answer


Problem 29

CMOT Dibbler is an up-and-coming movie mogul. In a time when the rest of the movie industry rely on ticket sales as their only source of revenue, Dibbler had the bright idea of improving his profit by selling popcorns. He now has an even brighter idea of using statistics to estimate how popular his popcorns are.

He takes a simple random sample of 225 movie patrons. Of those, 100 like his popcorns and the rest do not. What is the 90% confidence interval for the proportion of people who like Dibbler's popcorn?

  • Choose one answer.
(a) 0.44 +/- 0.05443226
(b) 0.44 +/- 0.06618493
(c) 0.44 +/- 0.03309246
(d) 0.44 +/- 0.4963869
Answer


Problem 30

A 1996 poll of 1,200 African American adults found that 708 think that the American dream has become impossible to achieve. The New Yorker magazine editors want to estimate the proportion of all African American adults who feel this way. Which of the following is an approximate 90% confidence interval for the proportion of all African American adults who feel this way?

  • Choose one answer.
(a) (0.57 , 0.61)
(b) (0.56 , 0.62)
(c) Can't be calculated because the population size is too small.
(d) Can't be calculated because the sample size is too small.
Answer


Problem 31

A simple random sample of 3,500 people age 18 or over is taken in a large town to estimate the percentage of people in that town who read newspapers. It turns out that 2,487 people in the sample are newspaper readers. A 95% confidence interval for the percentage of people in that town who read newspapers is given by

  • Choose one answer.
(a) The 10% condition is not satisfied so a 95% confidence interval is meaningless
(b) (95%, 96%)
(c) (70.22% , 71.77%)
(d) (69.48%, 72.51%)
Answer


Problem 32

Suppose you know that among all Californians, the distribution of the number of burritos eaten per year is normal with mean 6.4 and standard deviation 2.0. A simple random sample of 100 Californians is taken. There is a 95% chance that the mean of the sample will be in the range:

  • Choose one answer.
(a) 6.4 +/- 0.04
(b) 6.4 +/- 2.0
(c) 6.4 +/- 0.2
(d) 6.4 +/- 0.02
(e) 6.4 +/- 0.4
(f) 6.4 +/- 4.0
Answer


Problem 33

Sandy and Rob wants to estimate the percentage of UCLA students who go to a dance club on the weekend. Suppose that they both pick a random sample and find p hat to 0.30. Sandy finds the 95% CI to be from 0.20 to 0.40 and Rob finds the CI to be from 0.28 to 0.32.

Why are the results different?

  • Choose one answer.
(a) Rob used a larger sample.
(b) Rob used a less biased sample.
(c) Sandy used a larger sample.
(d) Rob used a more representative sample.
Answer


Problem 34

Uncle Frank likes two things: fishing and confidence intervals. One day, Uncle Frank catches 25 fish out of a lake. We can assume each fish in the lake has an equal chance of being caught, so this behaves like a sample of 25. The mean of his sample is 5 lbs. The standard deviation of his sample is 2 lbs. Help him construct a 95% confidence interval to try to capture the true average weight of the fish in the lake.

  • Choose one answer.
(a) The confidence interval goes from 3.6 to 6.4
(b) The confidence interval goes from 1 to 9
(c) The interval goes from 4.2 to 5.8
(d) The confidence interval is 5.8 - 4.2 = 1.6
Answer


Problem 35

A medical group want to find out if a new drug is effective in lowering blood pressure. 600 people in the 50-70 age range volunteer to participate in the study and 225 volunteers are randomly selected. The subjects take the medication for six months, and their blood pressure is measured before and after taking the medication.

Average drop in blood pressure = 30 SD of drop in blood pressure = 2

We want to calculate the 90% CI for the change in blood pressures and interpret it. What is the best answer?

  • Choose one answer.
(a) We are 90% confident that if a larger sample had been used the blood pressure would be lowered more than 29.78 and 30.22 points.
(b) If we take 100 samples of size 225 and calculate the 90% confidence interval, 90 of them will include 30 within their boundary.
(c) We are 90% confident that for this sample of volunteers, this drug would help to lower the blood pressure between 29.78 and 30.22 points.
(d) We are 90% confident that this drug would help to lower the blood pressure between 29.78 and 30.22 in the population.
Answer


Problem 36

At a clinic, researchers are examining the effect of a new drug on lowering the level of blood pressure among men in the 65-75 age range. 400 people volunteer to participate in the study. Researchers randomly select 100 subjects and measure their blood pressure before taking the medication and six months after taking the medication. They find the 95% confidence interval for the difference in blood pressure to be (20, 35). What is the best interpretation of this interval?

  • Choose one answer.
(a) We are 95% confident that the average drop in the blood pressure of the patients in the sample is between 20 to 35 poitns.
(b) If this study was repeated 100 times, in 95 out of 100 instances, the confidence interval would be between 20 and 35.
(c) We are 95% confident that the average drop in blood pressure of the patients in the population is between 20 to 35 points.
(d) The probability that the average drop in blood pressure falls between 20 to 35 in the sample is 95%.
Answer


Problem 37

In a Gallup Poll article like the one I handed out in class, the authors said:

“For example, with a sample size of 1,000 national adults, (derived using careful random selection procedures), the results are highly likely to be accurate within a margin of error of plus or minus three percentage points. Thus, if we find in a given poll that President Clinton’s approval rating is 50%, the margin of error indicates that the true rating is very likely to be between 53% and 47%.

To be more specific, the laws of probability say that if we were to conduct the same survey 100 times, asking people in each survey to rate the job Bill Clinton is doing as president, in 95 out of those 100 polls, we would find his ratings to be between 47% and 53%. In only 5% of those surveys we would expect his rating to be higher or lower than that due to chance error. “

The interpretation of 95% confidence given above in the second paragraph is:

  • Choose one answer.
(a) Correct, because that is exactly what 95% confidence means.
(b) Incorrect, because the Gallup Poll samples are samples of convenience, not random samples.
(c) Incorrect, because that is what 99% confidence means, not 95% confidence.
(d) Incorrect, because the paragraph is implying all samples contain the same people.
Answer


Problem 38

A recent poll by the Pew Research Center found that 27% of voters in the U.S. would like to see President Bush run for a third term if the Constitution allowed it. A 95% confidence interval was calculated for this proportion and found to be (24.5%, 29.5%).

Which of the following is a valid interpretation of this confidence interval?

  • Choose one answer.
(a) We would be surprised to find that the true percentage of voters is higher than 30%.
(b) There's a 95% chance that the true percentage of voters is between 24.5% and 29.5%.
(c) We can't make an inference without knowing the sample size.
(d) If the survey were to be repeated many time, 95% of the surveys would find that the percentage was between 24.5% and 29.5%.
Answer


Problem 39

A national poll found that 44% of all Americans agreed that more attention should be paid to mental health of war veterans. How large should a simple random sample be in order to obtain a margin of error of +/- 0.03 (that is , +/- 3%) in a 95% confidence interval?

  • Choose one answer.
(a) 526
(b) 1052
(c) 100
(d) In order to calculate N, we need the p-value of the population.
Answer


Problem 40

A researcher works at a children's hospital where five to six thousand infants are delivered every year. He takes a random sample of 81 newborns and measures their weight. He finds the average weight to be 6.9 pounds and the standard deviation to be 0.9 pounds. Would it be reasonable to conclude that the average weight of the newbors for this hospital is seven pounds? We will define reasonable as being 95% confident.

  • Choose one answer.
(a) We cannot make a decision because we do not know how the histogram of the data looks like.
(b) No, it is not reasonable to make such a conclusion. The actual weight of the newborns in this country is less than seven pounds.
(c) Yes, it is reasonable to conclude that the average weight of the newborns in this country is seven pounds.
(d) We cannot make a decision because we do not have the standard deviation in the population.
Answer


Problem 41

A simple random sample of 1000 persons is taken to estimate the percentage of Democrats in a large population. It turns out that 543 of the people in the sample are Democrats. Is the following statement true or false? Explain

(51%, 57.5%) is approximately a 95% confidence interval for the sample percentage of democrats.

  • Choose one answer.
(a) False, that is the approximate confidence interval for p. There is no confidence interval for the sample proportion.
(b) True, we did the computations and those are approximately the numbers for the confidence interval for p.
(c) True, that is the confidence interval for the sample mean.
(d) False, the confidence interval for the sample proportion should be smaller than that.
Answer

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