Statistics proctored exam study guide

Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (c) Make a box-and-whisker plot.

*See box-and-whisker plots*

Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice caseloads brought before the federal courts involving the businesses. Note: Contracts cases involve disputes over contracts between businesses. (SALT uses C for "Contracts," GT for "General torts (personal injury)", AL for "Asbestos liability," OPL for "Other product liability," and AO for "All other.") a) Make a Pareto chart of the caseloads. *See chart*

*See graph*

Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice caseloads brought before the federal courts involving the businesses. Note: Contracts cases involve disputes over contracts between businesses. (SALT uses C for "Contracts," GT for "General torts (personal injury)", AL for "Asbestos liability," OPL for "Other product liability," and AO for "All other.") (b) Make a pie chart showing the percentage of cases of each type. *See chart*

*See pie charts*

The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.76, given that a person has tuberculosis. The probability is 0.05 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will fall in the following categories. (Enter your answers to four decimal places.) (a) have tuberculosis and have a positive test

0.0304

The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.76, given that a person has tuberculosis. The probability is 0.05 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will fall in the following categories. (Enter your answers to four decimal places.) c) not have tuberculosis and have a positive test

0.0480

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy)... Are these outcomes mutually exclusive? Why? *See chart*

0.17... Yes. Choosing a green and blue M&M is not possible.

Given P(A) = 0.4 and P(B) = 0.6, do the following. a) If A and B are independent events, compute P(A and B).

0.24

Given P(A) = 0.4 and P(B) = 0.6, do the following. (b) If P(A | B) = 0.7, compute P(A and B).

0.42

The state medical school has discovered a new test for tuberculosis. (If the test indicates a person has tuberculosis, the test is positive.) Experimentation has shown that the probability of a positive test is 0.76, given that a person has tuberculosis. The probability is 0.05 that the test registers positive, given that the person does not have tuberculosis. Assume that in the general population, the probability that a person has tuberculosis is 0.04. What is the probability that a person chosen at random will fall in the following categories. (Enter your answers to four decimal places.) (b) not have tuberculosis

0.9600

Consider population data with 𝜇 = 30 and 𝜎 = 3. (a) Compute the coefficient of variation.

10%

Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (b) Find the interquartile range.

3.5

There is money to send three of seven city council members to a conference in Honolulu. All want to go, so they decide to choose the members to go to the conference by a random process. How many different combinations of three council members can be selected from the seven who want to go to the conference?

35

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information. (a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.)

6AM-12PM: 0.287 12PM-6PM: 0.124 6PM-12AM: 0.328 12AM-6AM: 0.261

For the following distribution, how many people had scores greater than X = 14? X: 20-25 f: 2 X: 15-19 f: 5 X: 10-14 f: 4 X: 5-9 f: 1

7

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: 58 52 68 86 72 66 97 89 84 91 91 92 66 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 (a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)

7 2 7 8 8 1 6 6 8 8 0 2 2 3 3 5 6 7 4 4 4 5 6 6 7 9 0 1 1 2 3 7

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 17% of your total grade, each major test is worth 21.5%, and the final exam is worth 40%. Compute the weighted average for the following scores: 88 on the lab, 100 on the first major test, 71 on the second major test, and 96 on the final exam.

90.125

You are manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order. b) What if the distribution for waiting times were bimodal? What might be some explanations?

A bimodal distribution for waiting times might exist if orders are filled at different rates during busy and slow periods.

What is the difference between a parameter and a statistic?

A parameter is a numerical measurement describing data from a population. A statistic is a numerical measurement describing data from a sample.

You are manager of a specialty coffee shop and collect data throughout a full day regarding waiting time for customers from the time they enter the shop until the time they pick up their order. (a) What type of distribution do you think would be most desirable for the waiting times: skewed right, skewed left, mound-shaped symmetric? Explain.

A skewed right distribution would be the most desirable because this would mean there are a lot of short waiting times and only a few long waiting times.

A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a campaign the most likely to win?" Fifteen people called in and nine said yes. What is the implied population?

All listeners of the radio talk show

What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg. (c) What is the implied population?

All new hybrid small cars

In a friendly study what is the difference between an individual and a variable?

An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured.

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience): (a) To conduct a preelection opinion poll on a proposed amendment to the state constitution, a random sample of 10 telephone prefixes (first three digits of the phone number) was selected, all the households, and all households from the phone prefixes selected were called.

Cluster sample

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience): (b) To conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used.

Convenience sample

Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice caseloads brought before the federal courts involving the businesses. Note: Contracts cases involve disputes over contracts between businesses. (SALT uses C for "Contracts," GT for "General torts (personal injury)", AL for "Asbestos liability," OPL for "Other product liability," and AO for "All other.") Which type of cases occur most frequently? *See chart*

General torts

Consider population data with 𝜇 = 30 and 𝜎 = 3. b) Compute an 88.9% Chebyshev interval around the population mean.

Lower Limit: 21 Upper Limit: 39

Consider the following measures: mean, median, variance, standard deviation, and percentile. b) Which measures utilize actual data values regardless of relative position? (Select all that apply.)

Mean, variance, standard deviation

Consider the following measures: mean, median, variance, standard deviation, and percentile. (a) Which measures utilize relative position of the data values? (Select all that apply.)

Median, percentile

What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg. (a) Identify the variable.

Miles per gallon

A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a campaign the most likely to win?" Fifteen people called in and nine said yes. What is the variable?

Opinion of a caller

What is the average miles per gallon (mpg) for all new hybrid small cars? Using Consumer Reports, a random sample of such vehicles gave an average of 35.7 mpg. (b) Is the variable quantitative or qualitative?

Quantitative

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience): (d) Subscribers to a new smart phone app that streams songs were assigned numbers. Then a sample of 30 subscribers was selected by using a random-number table. The subscribers in the sample were invited to rate the process for selecting the songs in the playlist.

Simple random sample

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience): e) To judge the appeal of a proposed television sitcom, a random sample of 10 people from each of three different age categories was selected and those chosen were asked to rate a pilot show.

Stratified sample

Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience): (c) To maintain quality control in a brewery, every 20th bottle of beer coming off the production line was opened and tested.

Systematic sample

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information. b) Do the probabilities add up to 1? Why should they?... What is the sample space in this problem?

Yes, because they cover the entire sample space... The entire day

How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: 58 52 68 86 72 66 97 89 84 91 91 92 66 68 87 86 73 61 70 75 72 73 85 84 90 57 77 76 84 93 58 47 b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote?

Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds).

A radio talk show host asked listeners to respond either yes or no to the question, "Is the candidate who spends the most on a campaign the most likely to win?" Fifteen people called in and nine said yes. Can you detect any bias in the selection of the sample?

Yes, voluntary response. Those with the strongest opinions are most likely to call in.

M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Suppose you have a large bag of plain M&M candies and you choose one candy at random. b) Find P(yellow candy or red candy)... Are these outcomes mutually exclusive? Why? *See chart*

Yes. Choosing a yellow and red M&M is not possible... 0.81

The output shown in the given JMP applet summarizes the distribution of number of calories per serving for 65 different candy bars. Use the JMP output to answer the following questions. *See JMP Applet*

a) The correct answer is 0.08. Adding the number of candy bars for the intervals in the histogram that correspond to greater than 400 calories results in 4 + 1 = 5. The proportion relative to the total number of candy bars is then 5/65 = 0.08. (b) The correct answer is 0.88. Adding the number of candy bars for the intervals in the histogram that correspond to less than 300 calories results in 1 + 8 + 29 + 19 = 57. The proportion relative to the total number of candy bars is then 57/65 = 0.88. (c) The correct answer is 51%. A reasonable way to estimate this percentage is to take half of the number of candy bars for the interval from 150 to 200 (to estimate those that are between 175 and 200), then add this to the number for the interval 200 to 250, and determine this percentage. The number of candy bars between 175 and 200 is approximately 8/2 = 4, so the number that are between 175 and 250 is approximately 4 + 29 = 33. This is (33/65) · 100% = 51% of the total number of candy bars. (d) The correct the shape of the distribution is skewed to the right (positively skewed). The distribution has a long tail on the right hand side, so this distribution would be described as skewed to the right.

Consider the following ordered data. 6 9 9 10 11 11 12 13 14 (a) Find the low, Q1, median, Q3, and high.

low: 6 Q1: 9 median: 11 Q3: 12.5 high: 14

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Round your mean to four decimal places.) 145 154 170 173 184 182 183 184 182 170 182 167 154 143

mean: 169.5000 median: 171.5 mode: 182