Math 219 Final Review

1. Multiple Choice: Using the pie chart below for the work status for a sample of 191 students: The percentage who are not employed is:

a. slightly less than 25% b. slightly more than 50% c. about 33% d. slightly less than 50% e. about 63%

2. Multiple Choice: The histogram shows a distribution that is:

a. uniformly distributed c. skewed left b. bell-shaped d. skewed right

3. When the data has extreme highs or lows, which is the best measure of central tendency? What is the best measure of spread (dispersion)?

4. Multiple Choice: There are two 6th grade classes at a middle school. Each class has 15 boys and 15 girls. In one class the mean height of students is 64 inches. From the information provided, what must be true about the mean height for the students in the other class? (A) The mean height for the students in the other class is 64 inches.

(B) The mean height for the students in the other class is less than 64 inches.

(C) The mean height for the students in the other class is more than 64 inches.

(D) The mean height for the students in the other class cannot be determined.

5. Multiple Choice: A teacher wants to know if students at a particular middle school are in favor of a new

school policy that allows students to carry cell phones during school hours. The teacher is not able to ask the opinion of every student at the school, so she needs to select an appropriate sample of the students. The best way to do this is for the teacher to ask: (A) Students at a randomly selected table from all of those in the lunch room.

(B) Students randomly selected from a list of all students at the school.

(C) Students selected by the principal.

(D) Students she can select and talk to between classes.

6. Multiple Choice: Researchers were interested in looking at air quality in different regions of the United States. The following dotplot represents the number of days in a certain month that the air quality was unhealthy for eighteen cities in the Midwest.

Which of the following is the boxplot for these data?

a.

c.

b.

d.

7. Multiple Choice: An advertisement makes the claim: “Lighter shoes make you run faster.” Of the following, which is the best way to investigate this claim? (A) Choose the records of the top twenty runners who are wearing the lighter shoes and compare their times to run 400 meters before and after they began wearing the shoes. (B) Choose twenty runners and select ten at random to wear lighter shoes and have the other ten wear heavier shoes to run 400 meters and compare their times. (C) Choose twenty runners at random and have the women wear the lighter shoes and the men wear the heavier shoes to run 400 meters and compare their times. (D) Choose to observe the results of 400-meter races for the next year and see how many winners are wearing the lighter shoes

8. Multiple Choice: This histogram shows a distribution that is

a. uniformly distributed c. skewed left b. bell-shaped d. skewed right

Use the graphs below to answer questions 9 – 11.

A.

B.

C.

9. The mean is less than the median. ________

10. The mean is greater than the median. ________

11. The mean is approximately equal to the median. ________ _________________________________________________________________________________________ 12. Which of the two dotplots has a larger standard deviation?

_________________________________________________________________________________________ 13. Below are dot plots for three different data sets. The standard deviations for these three data sets are

given in the following table. Looking at the dot plots and without calculating the standard deviations, match the data sets to the standard deviations.

_________________________________________________________________________________________ 14. Which class quiz scores had more variability? Explain.

A. B.

_________________________________________________________________________________________ 15. Here is a set of sample data of December temperatures in Chicago. 12 14 10 12 20 15 21 16 11 12 Find the mean, median, range, variance, and standard deviation.

Standard deviation

Data Set

5.9

3.3

2.3

16. Below are the restraint ratings given online using a scale 0 – 3.

rating frequency

0 3 1 5

2 12

3 46

a) Before doing any calculations, the mean for this b) Calculate the mean. data must be between what two values?

_________________________________________________________________________________________ 17. Multiple Choice: Disney wants to survey 200 guest who attend Disneyland on New Year’s Day on what they

thought of the fireworks. Which one of the following ways should they use to select a representative sample of adults from 100 guests?

a. Go to 10 different rides and ask 20 guests waiting in line.

b. Randomly select 20 employees, ask them to give 5 guest the survey they find in the park after the fireworks show.

c. Ask every 50th guest exiting the park.

d. Ask the first 20 guest that exit that park at 5 different exits.

_________________________________________________________________________________________ 18. Multiple Choice: Which is an example of cluster sampling? What are the others?

a. Select every 25th person who enters a movie.

b. Randomly choose 4 out of 16 CSU campuses and survey all statistics majors from those campuses.

c. Randomly choose 100 statistics students from each of the 16 CSU campuses.

d. Randomly choose 100 student ID numbers from students at SAC.

_________________________________________________________________________________________ 19. Multiple Choice: 23 math majors, 32 music majors and 45 history majors are randomly selected from 375

math majors, 526 music majors and 743 history majors at the state university. What sampling technique is used?

a. volunteer b. convenience c. simple random d. cluster e. stratified

_________________________________________________________________________________________ 20. Order the scatterplots by their correlation coefficient (least to greatest).

a.

b.

c.

21. For which of the following scatterplots is the correlation coefficient closest to 0?

_________________________________________________________________________________________ 22. Multiple choice: A scatterplot summarizing a sample of 21 bills at a restaurant, versus the corresponding

tip left for the server, is shown below. One of the points is labeled A.

If the labeled point A is removed, which of the following statements is true?

a. The correlation coefficient increases and the slope of the least squares regression line is unchanged.

b. The correlation coefficient decreases and the slope of the least squares regression line is unchanged.

c. The correlation coefficient increases and the slope of the least squares regression line increases.

d. The correlation coefficient decreases and the slope of the least squares regression line increases.

e. The correlation coefficient increases and the slope of the least squares regression line decreases.

A

23. The results of a least square regression line is found for a sample of 21 bills at a restaurant, versus the corresponding tip left for the server. Find the predicted tip left for a server on a $50.00 food bill.

_________________________________________________________________________________________ 24. Multiple Choice: A popular smartphone application keeps track of the number of games played and the

number of games won on the phone. The outcome of one game is independent from one game to the next and is based on the skill of the player. Let X = the number of games that have been won out of 200 games. Under which of the following situations would X be a random variable with a binomial distribution. a. A group of 10 players of different skill levels were each allowed to play the game 20 times in a row.

b. A group of players with different skill levels were each allowed to play the game until they lost 3 games and this resulted in 200 games played.

c. Two players of different skill levels competed by allowing one player continue until a game was lost, then the other player to continue until the game was lost, and so on, until 200 games were played.

d. Two players of equal skill level each played one game a day for 100 days and their skill level did not change from day to day.

_________________________________________________________________________________________ Determine if 17 – 20 are binomial (answer with yes or no). Explain why if NO.

25. Selecting 5 balls with replacement from a box that contains 100 balls, 60 of which are blue and the rest are red.

26. Selecting 5 balls without replacement from a box with 100 balls, 60 of which are blue and the rest are red.

27. Rolling a die 50 times.

28. Guessing on a true/false test with 20 questions. _________________________________________________________________________________________ Use the following for 21 – 25: A recent news report had found that 68% of all internet searches use Google (a website used for search). Suppose a random sample of 50 searches is taken from a database that contains records of internet activity and searches.

29. What is the probability that exactly 25 searches are conducted on Google?

30. What is the probability that at least 40 searches are conducted on Google?

31. How likely is it that less than 30 searches are conducted on Google?

32. On average how many searches out of 50 should we expect to be conducted on Google? With what standard deviation?

33. Would it be unusual for 45 of the searches to be conducted using Google? Explain.

Dependent Variable: Tip

Independent Variable: Bill

Tip = 0.41809921 + 0.14821403 Bill

R (correlation coefficient) = 0.88267172

Sample Size 21

34. Let X = the number of points that can be scored on 1 question of a statistics exam. Below is the probability distribution of how students did

x 0 1 2 3

P(x) .13 .21 .55

Find the following: a) P (at most 2) b) P(at least 1) c) P(more than 0) d) P(exactly 3) e) E(x) or 𝜇

_________________________________________________________________________________________ 35. Find the expected gain or loss

a) for an insurance company, if a life insurance premium on a $100,000 policy cost $400, and the chance of death during the term is 0.003.

b) per ticket for a raffle with a grand prize of a $2000 television and two second prizes of a $250 mobile phone. A total of 1000 tickets were sold for $5 each.

_________________________________________________________________________________________ 36. An automobile insurance company has determined the probabilities for various claim amounts for drivers

age 21 – 26.

Amount of Claim (to the nearest

$1000) Probability

a. Calculate the expected value in and describe what it means in practical terms.

b. What is the minimum amount of money the insurance

company should charge to guarantee that they do not lose money.

0 0.60 1000 0.20

2000 0.15

3000 0.03

4000 0.01

5000 0.01 _________________________________________________________________________________________ 37. One person is randomly selected. Using the contingency table, find:

men women doctors 25 5 lawyers 50 30 teachers 25 65

a) P(doctor or man) d) P(man and lawyer)

b) P(doctor or teacher) e) P(woman given doctor)

c) P(man)

38. A survey of 46 college athletes found that 24 played volleyball, while 22 played basketball. a) If we pick one athlete survey participant at random, what is the probability they play basketball?

b) If we pick 2 athletes at random (without replacement), what is the probability we get one

volleyball player and one basketball player?

c) If we pick 3 athletes at random (without replacement), what is the probability they all play volleyball?

__________________________________________________________________________________________ 39. A hat contains 2 red apples and 3 green apples. A bucket contains 7 red apples and 3 green apples.

a. A container is selected at random and an apple is drawn out. What is the probability that it will be a red apple?

b. A green apple is selected from the bucket and eaten. A second apple is to be selected from

the bucket. What is the probability that this second apple will be red?

c. Two different apples are selected from the hat. What is the probability that both are green?

__________________________________________________________________________________________ 40. A certain dataset of systolic blood pressure measurements has a mean of 80 and a standard deviation of 3.

Assuming the distribution is bell-shaped and we randomly select a measurement:

a) What percentage of measurements are between 71 and 89?

b) What is the probability a person’s blood systolic pressure measures more than 89?

c) What is the probability a person’s blood systolic pressure being at most 75?

d) We should expect 15% of patients have a blood pressure below what measurement?

e) Would it be unusual for 3 patients to have a mean blood pressure measurement of more than 84? Explain.

__________________________________________________________________________________________ 41. A manufacturer knows that their items have a length that are skewed right, with a mean of 12.3 inches,

and standard deviation of 0.5 inches. If 47 items are chosen at random, what is the probability that their mean length is greater than 12.4 inches?

__________________________________________________________________________________________ 42. A particular fruit's weights are normally distributed, with a mean of 499 grams and a standard deviation of

14 grams. If you pick 10 fruits at random, then 2% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.

43. In bowling the higher the score the better. Assume scores are normally distributed. Suppose the mean bowling score is 155 with a standard deviation of 16 points. a. We will give a trophy for the best 5% of scores. What score must you get to receive a trophy? b. What is the probability that in a sample of 40 bowling scores, the mean will at most 150?

c. Suppose we have a sample of the Santa Ana Strikers’ bowling scores, but we don’t know that the

distribution is normally distributed. We do know Q1 = 125 and Q3 = 156. Would it be usual or unusual to have a score of 200?

__________________________________________________________________________________________ 44. In golf lower the golf score the better. Suppose the mean golf score is 77 with a standard deviation of 3

strokes.

a. We will give a trophy for the best 5% of scores. What score must you get to receive a trophy?

b. Would a golf score of 70 be ordinary, a mild outlier, or an extreme outlier? __________________________________________________________________________________________ 45. Multiple Choice: The effectiveness of a blood-pressure drug is being investigated. An experimenter finds

that, on average, the reduction in systolic blood pressure is 62.5 for a sample of size 25 and standard deviation 18.2. Which of the following estimates how much the drug will lower a typical patient's systolic blood pressure (using a 99% confidence level).

a) 0.625 ± 2.797√0.182(1−0.182)

25

b) 62.5 ± 2.797 (18.2

√25)

c) 0.625 ± 2.576√0.182(1−0.182)

25

d) 62.5 ± 2.576 (18.2

√25)

e) 62.5 ± 2.581 (18.2

√25)

__________________________________________________________________________________________ 46. A political candidate has asked you to conduct a poll to determine what percentage of people support her.

If the candidate only wants a 8% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people.

__________________________________________________________________________________________ 47. A sample of size 20 was taken from a very large population in order to estimate a proportion, 𝑝. The

sample was found to have a proportion of �̂� = 0.6. Can we use the apply the normal distribution to estimate 𝑝 in this situation? Why or why not?

48. Multiple Choice: Suppose we are 95% confidence that interval from 0.205 to 0.305 contains the true population proportion of students who will complete the review for a final. What does 95% confident mean in this statement?

a. If we repeated the same random sampling process many times over, the interval from 0.205 to 0.305 will capture the sample proportion of students about 95% of the time.

b. There is a 95% chance that the interval 0.205 to 0.305 will capture the sample proportion of students who complete the review.

c. The interval from 0.205 to 0.305 will capture about 95% of the population who complete the

review.

d. There is a 95% probability that the interval from 0.205 to 0.305 actually contains the true population proportion of students who complete the review.

e. If we repeated the same random sampling process many times over, approximately 95% of all our

interval estimates will actually contain the true population proportion of students who complete the review.

__________________________________________________________________________________________ 49. In a recent poll, 380 people were asked if they liked dogs, and 37% said they did.

a. Find the margin of error of this poll at the 90% confidence level.

b. Find the confidence interval using the margin of error you found in part a. __________________________________________________________________________________________ 50. Carrie is running for mayor in her local city election. In order to win, she must earn over 50% of the votes.

So, Carrie decides to hire a couple of Statistics students to help her measure the progress in her campaign through polling. She is hoping to find sufficient evidence (α=0.05) that she will in fact win the election with more than 50% of the vote. The Statistics students test the following hypotheses, where p represents the proportion of all voters who will vote for Jemmy. Which of the following statements would be true if a Type I error is made? (Select all that apply.)

a. Carrie ends up winning the election. b. The students find a p-value less than 0.05 c. Carrie ends up losing the election. d. The students find a p-value greater than 0.05 e. The students make the conclusion that Carrie does not have more than 50% of the vote. f. The students make the conclusion that Carrie will have more than 50% of the vote.

__________________________________________________________________________________________ 51. A local high school gives its Algebra 2 students the same final exam every year. From 2000 to 2010, the

average score on the exam was a 68. In 2017, the average score was at a 75. Which test would be most appropriate to test if there is sufficient evidence to show that the students at the school have improved since the last decade? Write the appropriate hypothesis.

52. Multiple Choice: A commonly cited standard for one-way length (duration) of school bus rides for elementary school children is 30 minutes. A local government office in a rural area conducts a study to determine if elementary schoolers in their district have a longer average one-way commute time. If they determine that the average commute time of students in their district is significantly higher than the commonly cited standard they will invest in increasing the number of school busses to help shorten commute time. What would a Type 2 error mean in this context? a) The local government decides that the average commute time is 30 minutes.

b) The local government decides that the data provide convincing evidence of an average commute time

higher than 30 minutes, when the true average commute time is in fact 30 minutes.

c) The local government decides that the data do not provide convincing evidence of an average commute time higher than 30 minutes, when the true average commute time is in fact higher than 30 minutes.

d) The local government decides that the data do not provide convincing evidence of an average commute

time different than 30 minutes, when the true average commute time is in fact 30 minutes.

_________________________________________________________________________________________ 53. Matching: Each is used once. Decide which type of test would be most appropriate for each of these.

a. A higher percentage of Amazon shoppers get free shipping than the percentage of eBay shopper who get free shipping.

I. Two sample t-test

II. Matched pairs

b. MacBook owners spend more online than Microsoft Surface owners. III. Two proportion z-test

c. Buying a smartphone is less expensive online than in a retail store. IV. Chi-squared test for independence

d. Netflix, Hulu, and Amazon Prime members all spend the same mean number of hours per week watching Video.

V. ANOVA

e. Income level (poor, middle class, wealthy) and clothing store you shop at are related.

_________________________________________________________________________________________

54. Multiple Choice: In a random sample of high school seniors, the proportion who use text messaging was 0.88. In a random sample of high school freshmen, this proportion was 0.68. Researchers found the difference in proportions to be statistically significant and obtained one of the following numbers for the p-value. Which is it? a) 0.03

b) 0.20

c) 0.78

d) 1.56

e) 0.12

_________________________________________________________________________________________

55. Multiple Choice: Which hypotheses are most appropriate?

Claim: The cost of a generic medication is significantly lower than its name brand version.

a. Ho : cost of generic and cost of name brand are independent Ho : cost of generic and cost of name brand are associated

b. Ho : cost of generic and cost of name brand are associated H1 : cost of generic and cost of name brand are independent

c. Ho : cost of generic and cost of name brand are not linearly correlated

H1 : cost of generic and cost of name brand are linearly correlated

d. Ho : µd = 0 difference = generic - name brand version H1 : µd > 0

e. Ho : µd = 0 difference = name brand version - generic

H1 : µd > 0

________________________________________________________________________________________

56. A study was conducted to investigate how texting on a mobile device impairs driving ability. To address this issue, 126 participants drove an instrumented research vehicle on a closed driving course. The participants were randomly divided into the following groups: Control: No text messages were sent or received on their mobile device. Typing: Driver composed a story on their mobile device. Reading: Driver read a story on their mobile device. To measure impairment of driving ability, each driver was asked to maintain an average speed of 30 miles per hour through the four-mile course. At a random time, a green light over the front windshield flashed and the driver was asked to respond by pressing a button on the steering wheel. The response time was recorded by an instrument in the vehicle and are summarized in the boxplots to the right. a) Do the boxplots on the previous page suggest that texting while driving affects response time? Explain.

b) Use a 0.05 level of significance and the output below to test the claim that texting has an effect on the mean response time. ANOVA table

Source DF SS MS F-Stat P-value

Columns 2 395.8153 197.90765 186.09048 <0.0001

Error 375 398.81336 1.0635023

Total 377 794.62866

__________________________________________________________________________________________

57. More than 36% of workers indicate that they are dissatisfied with their job. Express the null and alternative hypotheses in symbolic form for this claim (enter as a percentage).

58. The mean weight of female dancers in a local modern dance company is less than 143 lbs. Express the null and alternative hypotheses in symbolic form for this claim.

__________________________________________________________________________________________

59. A researcher wanted to know whether there is an association between position for a male or female boss when a person starts a new job. The researcher randomly sampled 1,000 employed adults living in City A. Each person was asked, “If you were to start a new job, would you prefer to have a male boss or a female boss?” The table below shows the results for City A.

Use a 0.10 level of significance and the output below to test the claim that preference for a male of female boss is independent of position.

Statistic DF Value P-value

Chi-square 2 1.1345921 0.5671

__________________________________________________________________________________________

60. Samoas, Tagalongs, and Thin Mints are the most popular types of Girl Scout cookies in a school. Students in a sixth-grade class want to know which of the three types of cookies their classmates like the most. They also want to know how the popularity of the three types of cookies compares between boys and girls. Data from a class survey are summarized in the bar graphs below:

a) Which of the three types of cookies is most popular for the class? Justify your response.

b) Which of the three types of cookies is least popular for the class? Justify your response.

c) Were girls or boys more variable in their choices for favorite cookie? Justify your response.

__________________________________________________________________________________________

61. Shortly after the Apollo 11 lunar landing on July 20, 1969 a survey revealed that 28% of Americans did not believe it had happened. You have a theory that people nowadays are just as cynical and distrustful of government as they were back then, so you randomly sample 75 people and find that 25 of them do not believe that the Apollo 11 landing actually happened.

a) Explain why the initial requirements have been met.

b) Test the claim that the percentage is the same as its 1969 value

Prefer Male Boss Prefer Female Boss

Management 16 17

Classified 32 28

Certificated 56 54

For 62 – 71 Read each question. Choose the appropriate test or interval. If a test is required, write out the hypotheses. Use the formulas or technology to find the “important” numbers and write the appropriate conclusion.

62. A Gallup telephone poll of 1240 teens conducted in 2001 found that boys were more likely than girls to play computer games, 77% to 65% respectively. An equal number of boys and girls were surveyed. Give a 95% confidence interval for the difference in game playing by gender.

63. Your friend thinks that men and women get tipped differently. Say in a sample of 8 men, they have an

average of $45 in tips with a standard deviation of 2. In a sample of 7 women, they have an average of $39 in tips with a standard deviation of 5. Is there evidence that men and women get tipped differently?

64. Students were bored and checked 6 bags of Fritos marked with a net weight of 35.4 grams. They

weighed the contents of each bag and came up with the following: 35.5, 35.3, 35.1, 36.4, 35.4, and 35.5. Is there evidence that the mean weight of bags of Fritos is less than advertised?

65. A survey of several randomly selected hospitals found that 16.6% of 223 recent births in Vermont

involved cesarean deliveries, compared with 18.8% of 186 births in New Hampshire. Is this evidence that the rate of cesarean births in the two states is different?

66. Among 23 golden hamster litters recorded, there was an average of 7.72 baby hamsters, with a

standard deviation of 2.5 hamsters per litter. Create a 90% confidence interval for the average size of hamster litters.

67. You have a friend that is running for president of a club against one other person. She wants to know

if she can expect to win. You take a random sample of 85 people and 45 say they will vote for your friend. Is there evidence that your friend will win?

68. A testing service is trying to decide if paper and online versions of a test give equivalent results. Ten

subjects took both a paper test and an online test. Create a 99% confidence interval for the average difference in test scores.

69. A study of auto safety determined the number of driver deaths per million vehicle sales for the model years 1995-1999, classified by type of vehicle. The data below are for 6 midsize models and 6 SUVs. Create a 95% confidence interval for the difference in driver death rates for the two types of vehicles.

70. A teacher thinks that 75% of students usually study for tests. She thinks this chapter is more difficult though. She takes a sample of 40 students and 35 of them say they are going to study for this chapter’s test. Create a 98% confidence interval for the proportion of students who are going to study for this test.

Paper 14 10 16 17 14 9 12 16 7 15

Online 13 13 8 16 11 12 12 16 14 14

Midsize 47 54 64 76 88 97

SUV 55 60 62 76 91 109

71. In 1974, the Bellevue-Stratford Hotel in Philadelphia was the scene of an outbreak of what later

became known as legionnaires’ disease. The cause of the disease was finally discovered to be bacteria that thrived in the air-conditioning units of the hotel. Owners of the Rip Van Winkle Motel, hearing about the Bellevue-Stratford, replace their air-conditioning system. The following data are the bacteria counts, in the air of eight rooms, before and after a new air-conditioning system was installed. Does the data provide evidence that the new system has succeeded in lowering the bacterial count?

Room Number 121 163 125 264 233 218 324 325

Before 11.8 8.2 7.1 14 10.8 10.1 14.6 14

After 10.1 7.2 3.8 12 8.3 10.5 12.1 13.7