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1960

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Statistics

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Feb 20, 2024

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Chapters 1-6 1. Classify each variable as qualitative (categorical) or quantitative (numerical) a. Marital status of nurses in a hospital. Time 1t takes 10 people to complete a New York Times crossword puzzle. Weights of lobsters in a restaurant tank. Colors of cars in a shopping center parking lot. Amount of garbage (in pounds) discarded by residents of a high-rise apartment complex. © oo 2. Classify each sample as random, systematic, stratified, cluster, volunteer, or convenience a. All fast-food workers at a randomly selected fast-food restaurant are selected and asked how many hours per week they work. b. A group of unmarried men are selected using random numbers and asked how long it has been since their last date. c. Every 100" hamburger manufactured is checked to determine its fat content. d. Mail carriers of a large city are divided into four groups according to gender (male or female) and according to whether they walk or ride on their routes. Then 10 are selected from cach group and interviewed to determine whether they have been bitten by a dog in the last year. ¢. People arc asked to phone in their response to a survey question. 3. Identify cach study as being observational or experimental. Identify the individuals, sample, population, RV, EV, and treatments if applicable. a. A study was conducted to determine if crocodiles raised in captivity (i.c., in a zoo) grew faster than crocodiles living in the wild. b. Pecople who walk at least 3 miles a day are randomly selected, and their blood triglyceride levels arc measured in order to determine if the number of miles that they walk has any influence on these levels c. Subjects were randomly assigned to two groups, and one group was given an herb and the other a placebo. After 6 months, the numbers of respiratory tract infections each group had were compared. d. A rescarcher stood at a busy intersection to see if the color of the car that a person drives is related to running red lights. ¢. Three groups of gamblers were randomly selected. The first group was given $25 in casino money. The second group was given a $25 coupon for food. The third group was given nothing. After a trip to the casino, each group was surveyed and asked their opinion of their casino experience. 4. Identify each experiment as a completely randomized design, matched pairs design, or block design. a. To explore the effects of red wine on heart health, 100 volunteers are recruited. Half are to drink one glass of red wine a day with dinner for a month. The other half are to abstain from any alcohol for a month. The diets of all volunteers are otherwise the same. Women and men may respond differently to wine. Forty of the volunteers are women and 60 are men, so the rescarchers separately randomly assign half of the women to the wine group and half the men to the wine group. The remaining volunteers are assigned to the no alcohol group. b. One method of brewing coffee is the pour over. Ground coffee 1s placed in a filter-lined dripper. Hot water is poured over the coffee and allowed to drip into the carafe. A coffee shop carries three brands of dripper, each brand differing in shape and the placement of holes through which the coffee drips. Some experts believe that moistening the filter with hot water before filling

with grounds affects flavor, so the coffee shop plans the following experiment. For cach brand of dripper, coffee 1s to be brewed both with the filter moistened and with the filter dry. A trained barista will brew two cups of coffee for cach of the six combinations of dripper and wet/dry filter. A panel of trained tasters scores cach cup for flavor on a scale of 1 to 10 with higher scores indicating better flavor. c. Suppose researchers want to know how a new diet affects weight loss compared to a standard diet. Since this experiment only has two treatment conditions (new diet and standard diet), they can usc a matched pairs design. They recruit 100 subjects, then group the subjects into 50 pairs based on their age and gender. Then, within each pair, one subject will randomly be assigned to follow the new diet for 30 days and the other subject will be assigned to follow the standard diet for 30 days. At the end of the 30 days, researchers will measure the total weight loss for each subject. Chapter 8 1. Give an example of an invalid way to measure and a valid way to measure for each situation a. Measure a healthy lifestyle b. Mecasure a person’s intelligence c. Measure a person’s pain tolerance Chapters 10 - 11 1. Construct a bar graph showing the frequency of each country winning the Men’s World Hockey Championship given in the list below. USSR: 4 Canada: 6 Czechoslovakia: 1 Finland: 1 Sweden: 7 Czech Republic: 6 Russia: 5 Slovakia:1 2. Construct a pie chart for the types of crimes commonly committed in the United States Theft: 55% Assault: 8% Burglary: 20% Rape & Homicide: 1% Motor Vehicle Theft: 11% Other: 5% 3. Construct a stem-and-leaf-plot for the number of public libraries in operation for 15 sclected states 102 176 210 142 189 176 108 113 205 209 184 144 108 192 176 4. Construct a line graph displaying the number of new Broadway shows between the years 2004 and 2013 Season: 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 New Shows: 39 39 35 39 43 39 42 41 46 44 5. Construct a histogram for the weight of 30 players on a football team. Use 10 classes starting at 200. 213 248 203 218 254 202 239 233 224 219 232 215 249 258 235 206 221 238 227 262 219 223 254 230 233 246 220 223 256 263

Chapters 12 1. Find the mean, median, range (max-min), IQR, variance, and standard deviation for cach of the following sets. a. 14 24 51 92 157 148 30 3 0 0 4 3 11 2. Construct two boxplots for the number of hours worked by 12 part-time employees at a toy store before and after Christmas. Before: 38 16 18 24 12 30 35 32 31 30 24 35 After: 26 15 12 18 24 32 14 18 16 18 22 12 Chapter 13 1. Find the appropriate standard scores, percentiles, or observation values for each of the following a. The average number of vacation days for various countries has an average of 29.4 days and standard deviation of 8.6 days. 1. Canada gives 26 vacation days. What is Canada’s standard score? i1. What is Canada’s percentile? 111, How many days would it take to be in the top 5%°? 1v. What are the bounds for 68%, 95%, and 99.7%"? b. The average age when women get married is 24.6 years with standard deviation of 3.2 years. 1. Morgan is getting married at age 29. What is her standard score? Chapter 14 -15 What percentage of women are getting married who are older than Morgan? What percentage of women are getting married younger than 24 years of age? What percentage of women are getting married between 24 and 29 years of age? 1. For the following, draw the scatterplot and calculate the correlation coefficient. a. The average gas price per gallon and the cost of a barrel of oil are shown for a random selection of weeks 1in 2015. Oil ($) 51.91 60.65 59.56 52.86 45.12 4421 Gasoline ($) | 1.97 1.96 2.06 2.04 2.00 1.99 b. An environmentalist wants to determine the relationships between the numbers (in thousands) of forest fires over the year and the number (in hundred thousand) of acres burned. Fires 72 69 58 47 84 62 57 45 Acres 62 42 19 26 51 15 30 15

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2. Given the regression equation and correlation coefficient, answer the following. a. Gasoline =0.0009 * O1l + 1.9564; r=0.158 i. What is the price of gasoline when a barrel of oil is $57.62? ii. If gasoline is $2.03 per gallon, what do you expect the price of a barrel of oil to be? i11. What percentage of variation is accounted for by the regression equation? What percentage of variation 1s accounted for by the scatter of the points? b. Acres =1.0358 * Fires —31.46;r=0.771 1. How many acres (in hundred thousand) are burned when there are 52 (thousand) forest fires? i1. If 20 (hundred thousand) acres are burned, how many (thousand) forest fires do you expect there to be? i11. What percentage of variation is accounted for by the regression equation? What percentage of variation 1s accounted for by the scatter of the points? Chapters 17 -18 1. Given the table below, calculate appropriate probabilities. Surgical site Pneumonia Bloodstream Total Infection Infections Infections Hospital A 41 27 51 119 Hospital B 36 3 40 79 Hospital C 169 106 109 384 Total 246 136 200 582 a. Infection was at Hospital C b. Pneumonia Infection c. Hospital C and Pneumonia d. Hospital C or Pneumonia ¢. A patient has Pneumonia given they are at hospital C f. Given the patient has pneumonia, what is the probability they are at hospital C? g. Not at hospital C h. Not pneumonia 1. Assuming patients are independently chosen, what is the probability that two happen to have surgical site infections? 2. Find the sample space size for the following situations a. Three bands and two comedians are performing at a club over the weekend. Their times are flexible, so how many different arrangements are there for them to perform? b. In order to get to Columbia from Clemson, there are two main routes, one through Easley and Greenville or one towards Anderson to Greenville, in order to get you to SC-385. Then there are 3 main ways to get to Williams-Brice Stadium for the Tigers v. Gamecocks game. How many ways are there to get from Clemson to the Stadium? c. The tests for checking a piece of equipment are numbered 1-7. Any portion of tests, must be done such that the test numbers are in ascending order (i.e., tests 1, 3, 5, 7 are okay but 2, 1, 7, 4 is not). An inspector can only conduct 3 tests. How many ways are there for him to complete the tests?

d. In anew drug trial, 5 of 50 patients need to be randomly selected to take the new drug. How many ways are there for doing this? Chapter 20 — Find Expected Values for the Variable X 1. X 1 2 3 4 5 P(X) 0.1 0.3 0.1 0.2 0.3 2. X 5 10 15 20 P(X) 0.3 0.4 0.1 0.2 3. X 1 4 9 16 P(X) 3/8 2/8 1/8 2/8 4. X 10 11 12 13 14 P(X) 0.2 0.12 0.4 0.31 0.15 5. X 0 1 2 3 4 5 P(X) 0.27 0.28 0.2 0.15 0.08 0.02 Chapter 21 - Find the appropriate confidence interval 1. A patient complained that the cost to visit their doctor was too high. Out of a sample of 20 patients, the average doctor’s visit was $44.80 with a sample standard deviation of $3.53. Find a 95% confidence interval for the population mean. Interpret the interval. 2. A political analyst found that 43% of 300 randomly selected Republican voters believe that the federal government has too much power. Find a 95% confidence interval for the population proportion. Interpret the interval. 3. A survey of 90 randomly sclected families showed that 40 owned at least one TV. Find the 95% confidence interval for the population proportion. Interpret the interval. 4. The average weight of a sample of 40 minivans was 4150 pounds with a standard deviation of 480 pounds. Find a 99% confidence interval for the population mean. Interpret the interval.

5. The average age of 10 randomly selected insurance agents was 48.6 years with a standard deviation of 4.1 years. Find a 95% confidence interval for the population mean. Interpret the interval. Chapter 22 — Conduct a Significance Test for each of the following. Give the appropriate hypotheses, Test Statistic, p-value, and Conclusion statement. 1. A real estate agent believes the average closing cost of a new home is $6500 over the purchase price. She sclects 40 new homes with an average closing cost of $6600 and standard deviation of $120. Test her belief at the o = 0.05 significance level. . A survey in Men’s Health reported that 39% of cardiologists said that they took vitamin E supplements. A researcher took a sample of 100 cardiologists and found that 36 said they took vitamin E supplements. Test the claim that the proportion is smaller at the o = 0.05 significance level. . A Harris Poll found that 35% of people say they drink caffeinated beverages. A recent survey found 19 out of 48 do. Test the claim that the proportion is larger at the o = 0.02 significance level. A taxi company claims that drivers have an average of 12.4 years of experience. From a sample of 15 drivers, the average experience was 11.2 years with standard deviation of 2 years. Test the claim that the average years of experience is less than what the company believes at the a = 0.10 significance level. In a small city, the average age of robbery victims is said to be 63.5 years. Out of 20 recent victims, the average age was 63.7 years with standard deviation of 1.9 years. At the a = 0.05 significance level, test the claim that the average age 1s higher than originally believed. Chapter 24 — Conduct a Chi-Squared Significance Test for each of the following. Give the appropriate hypotheses, expected values, x 2 value, Degrees of Freedom, Table 24.1 value, and Conclusion statement. 1. 2. Is there an association between hospital and the number of infected patients? Use a. = 0.05 Do doctors feel differently about a new procedure compared to the nurses? Use o = 0.05 Prefer New Prefer Old No Preference Total Procedure Procedure Doctors 100 80 20 200 Nurses 50 120 30 200 Total 150 200 50 400 Surgical site Pneumonia Bloodstream Total Infection Infections Infections Hospital A 41 27 51 119 Hospital B 36 3 40 79 Hospital C 169 106 109 384 Total 246 136 200 582

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3. Is there an association between gender and mental disorders? Use o= 0.10 Anxiety Depression Schizophrenia Total Male 8 12 10 30 Female 12 9 3 24 Total 20 21 13 54 4. Is there an association between age and drug use? Use a.=0.10 Inhalants Hallucinogens Tranquilizers Total 12-17 16 9 5 30 18-25 22 30 8 60 26+ 13 18 10 41 Total 51 57 23 131 5. Is there an association between gender and type of car owned? Use a. = 0.05 Luxury Large Midsize Small Total Male 15 9 49 27 100 Female 9 6 62 14 91 Total 24 15 111 41 191

*All problems are sourced from the 10" Edition of Elementary Statistics: A Step-by-Step Approach by Allan G. Bluman and from the 91" Edition of Statistics Concepts and Controversies by David S. Moore and William I. Notz

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