Stats questions

Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon? a. 15 b. 20 c. 25 d. 35 e. 50

d

In a certain region, 94 percent of the people have a certain characteristic in their blood. Suppose a group of 45 people from the region are selected at random. Let the random variable BB represent the number of people in the sample without the characteristic. Random variable BB follows a binomial distribution with a mean of 2.7 people. Which of the following is the best interpretation of the mean? a. For all groups of 45 people, the average number of people without the characteristic is 2.7. b. Every group of 45 people will have 2.7 people with the characteristic. c. Every group of 45 people will have 2.7 people without the characteristic. d. On average, 2.7 people are selected until finding someone with the characteristic. e. On average, 2.7 people are selected until finding someone without the characteristic.

a

According to 2015 census data, 42.7 percent of Colorado residents were born in Colorado. If a sample of 250 Colorado residents is selected at random, what is the standard deviation of the number of residents in the sample who were born in Colorado? a. 6.75 b. 7.82 c. 10.33 d. 11.97 e. 61.17

b

Which of the following statements is true about a distribution that appears to have a gap when displayed as a histogram? a. The distribution must have an outlier. b. The distribution has a region between two data values where no data were observed. c. The distribution is approximately normal. d. The distribution cannot be symmetric. e. The distribution must be bimodal.

b

A player pays $15 to play a game in which a chip is randomly selected from a bag of chips. The bag contains 10 red chips, 4 blue chips, and 6 yellow chips. The player wins $5 if a red chip is selected, $10 if a blue chip is selected, and $20 if a yellow chip is selected. Let the random variable X represent the amount won from the selection of the chip, and let the random variable W represent the total amount won, where W=X−15. What is the mean of W ? a. 10.50 b. 4.50 c. -4.50 d. -6.50 e. -10.50

c

A chemist for a paint company conducted an experiment to investigate whether a new outdoor paint will last longer than the older paint. Fifty blocks made from the same wood were randomly assigned to be painted with either the new paint or the old paint. The blocks were placed into a weather-controlled room that simulated extreme weather conditions such as ice, temperature, wind, and sleet. After one month in the room, the blocks were removed, and each block was rated on texture, shine, brightness of color, and chipping. The results showed that the blocks painted with the new paint generally had higher ratings than the blocks painted with the old paint. However, an analysis of the results found that the difference in ratings was not statistically significant. What can be concluded from the experiment? a. There is not enough evidence to attribute the higher ratings to the new paint. b. The new paint will last longer than the old paint if used on wooden surfaces. c. The experiment is inconclusive because blocks from only one type of wood were used. d. The experiment is inconclusive because one month is not enough time for paint to weather. e. Because the blocks were randomly assigned to the type of paint, there is evidence that the new paint causes better ratings than the old paint.

a

Researchers are investigating the effect of pH level in water on the breeding habits of the moon jellyfish. As part of a laboratory experiment, they will randomly assign one of three treatments, low pH, medium pH, or high pH, to the water in the tanks that hold the jellyfish. a. Randomization tends to minimize the effects of uncontrolled variables, such as water temperature, so that such factors are not confounded with the treatment effects. b. Randomization will make up for improper experimental design, data collection, and analysis. c. Randomization makes the analysis easier since the data can be entered into the computer in any order. d. Randomization is required by statistical consultants before they will analyze the experiment. e. Randomization means that the experiment would not need to be replicated.

a

A researcher wanted to study the effects of a certain chemical on cell growth. The chemical was to be applied at two different doses, high and low, to two different cell types, strain A and strain B. Each combination of dose and cell type was to be replicated ten times. To have consistency from one replicate to the next, the researcher decided to use four lab technicians. One technician would be assigned the high dose with strain A. A second would be assigned the low dose with strain A. A third would be assigned the high dose with strain B. A fourth would be assigned the low dose with strain B. The assignment of lab technician to the replicates for a combination of dose and cell type would be randomized. A statistician told the researcher that the design could be improved by controlling confounding variables. Which of the following is potentially a confounding variable in this study? a. Chemical used b. Lab technician c. Dose d. Cell type e. Cell growth

b

A tennis ball was thrown in the air. The height of the ball from the ground was recorded every millisecond from the time the ball was thrown until it reached the height from which it was thrown. The correlation between the time and height was computed to be 0. What does this correlation suggest about the relationship between the time and height? a. There is no relationship between time and height. b. There is no linear relationship between time and height. c. The distance the ball traveled upward is the same as the distance the ball traveled downward. d. The correlation suggests that there is measurement or calculation error. e. The correlation suggests that more measurements should be taken to better understand the relationship.

b

Backstroke mean: 55.6 seconds, SD: 0.70 seconds Breaststroke mean: 63.3 seconds, SD: 0.92 seconds Butterfly mean: 54.4 seconds, SD: 0.94 seconds Freestyle mean: 50.2 seconds, SD: 0.76 seconds For each of the 4 stroke categories, consider a random variable representing the time of a randomly selected swimmer in that category. What is the standard deviation of the sum of the 4 random variables? a. .83 b. 1.67 c. 2.8 d. 3.32 e. 3.76

b

The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable SS has mean 7 and standard deviation 3. If R and S are independent, what are the mean and standard deviation of the distribution of R−S? a. Mean 3 and SD 1 b. Mean 3 and standard deviation 5 c. Mean 3 and standard deviation 7 d. Mean 17 and standard deviation 1 e. Mean 17 and standard deviation 5

b

A researcher in Alaska measured the age (in months) and the weight (in pounds) of a random sample of adolescent moose. When the least-squares regression analysis was performed, the correlation was 0.59. Which of the following is the correct way to label the correlation? a. 0.59 months per pound b. 0.59 pounds per month c. 0.59 d. 0.59 months times pounds e. 0.59 month pounds

c

A restaurant manager collected data on the number of customers in a party in the restaurant and the time elapsed until the party left the restaurant. The manager computed a correlation of 0.78 between the two variables. What information does the correlation provide about the relationship between the number of customers in a party at the restaurant and the time elapsed until the party left the restaurant? a. The relationship is linear because the correlation is positive. b. The relationship is not linear because the correlation is positive. c. The parties with a larger number of customers are associated with the longer times elapsed until the party left the restaurant. d. The parties with a larger number of customers are associated with the shorter times elapsed until the party left the restaurant. e. There is no relationship between the number of customers in a party at a table in the restaurant and the time required until the party left the restaurant.

c

Based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction? a. 25% b. 48% c. 50% d. 75% e. 100%

c

Based on the histogram, which of the following statements best describes the relationship between the mean and the median of the distribution of ages? a. The mean and the median are equal in value because the distribution is symmetric. b. The mean is most likely less than the median because the distribution is skewed to the right. c. The mean is most likely less than the median because the distribution is skewed to the left. d. The mean is most likely greater than the median because the distribution is skewed to the right. e. The mean is most likely greater than the median because the distribution is skewed to the left.

c

One student from a high school will be selected at random. Let A be the event that the selected student is a student athlete, and let B be the event that the selected student drives to school. If P(A∩B)=0.08 and P(B|A)=0.25, what is the probability that the selected student will be a student athlete? a. .02 b. .17 c. .32 d. .33 e. 3.13

c

The relationship between carbon dioxide emissions and fuel efficiency of a certain car can be modeled by the least-squares regression equation ln(yˆ)=7−0.045x⁡, where x represents the fuel efficiency, in miles per gallon, and yˆ represents the predicted carbon dioxide emissions, in grams per mile. Which of the following is closest to the predicted carbon dioxide emissions, in grams per mile, for a car of this type with a fuel efficiency of 20 miles per gallon? a. 1.8 b. 6.1 c. 446 d. 2697 e. 1,250,000

c

Which of the following statements about a least-squares regression analysis is true? A point with a large residual is an outlier. A point with high leverage has a yy-value that is not consistent with the other yy-values in the set. The removal of an influential point from a data set could change the value of the correlation coefficient. a. I only b. II only c. III only d. I and III only e. I,II, and III

c

x | 1234567 P(x) | 0.05 0.10 0.22 0.30 .18 0.12 0.03 At the company, the daily salary of a loan agent is $150 plus $50 per loan closed. Let Y represent the amount of money made by a randomly selected loan agent on a randomly selected day. Which of the following statements is NOT true? A. The mean of X is less than the mean of Y. b. The standard deviation of Y is approximately $71. c. The mean daily salary is greater than $350 per day. d. The standard deviation of X is less than the standard deviation of YY. e. The shape of the probability distribution of Y is unimodal and roughly symmetric.

c

An exponential relationship exists between the explanatory variable and the response variable in a set of data. The common logarithm of each value of the response variable is taken, and the least-squares regression line has an equation of log(yˆ)=7.3−1.5xlog⁡(y^)=7.3−1.5x. Which of the following is closest to the predicted value of the response variable for x=4.8x=4.8 ? a. 0.1 b. .68 c. 1.105 d. 1.26 e. 14.5

d

Data were collected on the ages, in years, of the men and women enrolled in a large sociology course. Let the random variables M and W represent the ages of the men and women, respectively. The distribution of M has mean 20.7 years and standard deviation 1.73 years. The distribution of W has mean 20.2 years and standard deviation 1.60 years. Of all of those enrolled in the course, 54 percent are men and 46 percent are women. What is the mean age of the combined distribution of both men and women in the course? a. 20.2 years b. 20.43 years c. 20.45 years d. 20.47 years e. 40.9 years

d

For a random sample of 20 professional athletes, there is a strong, linear relationship between the number of hours they exercise per week and their resting heart rate. For the athletes in the sample, those who exercise more hours per week tend to have lower resting heart rates than those who exercise less. Which of the following is a reasonable value for the correlation between the number of hours athletes exercise per week and their resting heart rate? a. .71 b. .00 c. -.14 d. -.87 e. -1.00

d

If the interval size is decreased from $200 to $100, which of the following must remain the same on the new histogram? a. The heights of the bars b. The widths of the bars c. The number of bars d. The sum of the frequencies e. The shape of the distribution

d

In 2014, 85 percent of households in the United States had a computer. For a randomly selected sample of 200 households in 2014, let the random variable CC represent the number of households in the sample that had a computer. What are the mean and standard deviation of CC ? a. The mean is 85 households, and the standard deviation is 0.36 household. b. The mean is 144.5 households, and the standard deviation is 5.05 households. c. The mean is 144.5 households, and the standard deviation is 13.04 households. d. The mean is 170 households, and the standard deviation is 5.05 households. e. The mean is 170 households, and the standard deviation is 0.36 household.

d

Mr. Ikeler conducted a study investigating the effectiveness of a new method for teaching a mathematics unit. He recruited 80 students at a college and randomly assigned them to two groups. Group 1 was taught with the new method, and group 2 was taught with the traditional method. Both groups were taught by the same teacher. At the end of the unit, an achievement test was administered and used to make a comparison of the two groups. What is the response variable in the study? a. The new teaching method b. The traditional teaching method c. The teacher in the study d. The score on the achievement test e. The 80 students

d

Researchers will use a well-designed experiment to test the effectiveness of a new drug versus a placebo in relieving symptoms of the common cold. Which of the following will provide evidence that the new drug causes relief of symptoms? a. The experiment cannot be used to show the new drug causes relief, only that it is related to relief. b. Any difference between the responses to the new drug and the placebo provides evidence that the new drug causes relief. c. The experiment cannot be used to show the new drug causes relief because the new drug is not being compared to an older drug. d. The difference between the responses to the new drug and the placebo must be shown to be statistically significant to provide evidence that the new drug causes relief. e. Relief of symptoms would need to occur in all subjects who take the new drug and in none of the subjects who take the placebo to provide evidence that the new drug causes relief.

d

The owner of a food store conducted a study to investigate whether displaying organic fruit at the front of the store rather than at the back of the store will increase sales of the fruit. At the beginning of each week, the organic fruit display was randomly assigned to either the front or the back of the store, and sales for the week were recorded. At the end of 12 months, the owner determined that the average weekly sales of organic fruit displayed at the front of the store were greater than the average weekly sales of organic fruit displayed at the back of the store. The difference was statistically significant. What can be concluded from the study? a. Sales of organic fruit generally increased over the 12-month period. b. Shoppers will buy more organic fruit each day if they see it when they first enter the store. c. Any conclusion is problematic because the different types of fruit were not taken into account as part of the study. d. Placing the display at the front instead of the back of the store causes an increase, on average, of weekly sales of the organic fruit. e. Weekly sales of organic fruit will always be greater when the fruit is displayed at the front of the store rather than the back of the store.

d

The random variable X has mean 12 and standard deviation 3. The random variable W is defined as W=7+2X. What are the mean and standard deviation of W? a. The mean is 24, and the standard deviation is 6 b. The mean is 24, and the standard deviation is 13. c. The mean is 31, and the standard deviation is 3. d. The mean is 31, and the standard deviation is 6. e. The mean is 31, and the standard deviation is 13.

d

Which of the following statements is the best description of the distribution of scores? a. The distribution is roughly symmetric. b. The distribution is roughly uniform. c. The distribution is skewed left. d. The distribution is skewed right. e. The distribution is bimodal.

d

A botanist found a correlation between the length of an aspen leaf and its surface area to be 0.94. Why does the correlation value of 0.94 not necessarily indicate that a linear model is the most appropriate model for the relationship between length of an aspen leaf and its surface area? a. The value must be exactly 1 or −1 to indicate a linear model is the most appropriate model. b. The value must be 0 to indicate a linear model is the most appropriate model. c. A causal relationship should be established first before determining the most appropriate model. d. The value of 0.94 implies that only 88% of the data have a linear relationship. e. Even with a correlation value of 0.94, it is possible that the relationship could still be better represented by a nonlinear model.

e

A certain factory that manufactures office chairs has a quality control process to identify defective chairs. The binomial random variable D represents the number of chairs in a sample of chairs that are defective. The mean of D is 10 chairs and the standard deviation is 3 chairs. Based on the distribution of D, which of the following would be an accurate interpretation of the value 0.1 ? a. The total number of defective chairs made b. The total number of non-defective chairs made c. The relative frequency of the sample size to the population of chairs d. The probability of identifying a non-defective chair e. The probability of identifying a defective chair

e

A company that ships crystal bowls claims that bowls arrive undamaged in 95 percent of the shipments. Let the random variable GG represent the number of shipments with undamaged bowls in 25 randomly selected shipments. Random variable GG follows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean? a. Every shipment of 25 bowls will have 23.75 undamaged bowls. b. Every shipment of 25 bowls will have 23.75 damaged bowls. c. On average, the company receives 23.75 shipments before receiving the first shipment with a damaged bowl. d. For all possible shipments of size 25, the average number of damaged shipments is equal to 23.75. e. For all possible shipments of size 25, the average number of undamaged shipments is equal to 23.75.

e

A local employer asked for help selecting a new type of desk chair. Thirty employees volunteered, and each employee used the new desk chair for two weeks and the current desk chair for two weeks. To determine which chair was used first, a coin was flipped for each employee. Heads represented using the new chair first, and tails represented using the current chair first. At the end of each two-week period, the employees were asked to rate their satisfaction with the new chair. Which of the following best describes this study? a. It is not a well-designed experiment because employees were allowed to volunteer instead of being randomly selected. b. It is not a well-designed experiment because only one new chair was used. At least two new treatments must be used. c. It is not a well-designed experiment because each employee was assigned both treatments, and each employee should be assigned only one. d. It is not a well-designed experiment because using a coin flip does not guarantee that fifteen employees will use each chair first. e. It is a well-designed experiment because there is random assignment, replication, and comparison of at least two treatment groups.

e

According to a survey about how workers get to work in Wyoming, 77 percent of workers get to work by driving alone, 11 percent get to work by carpooling, 4 percent get to work by walking, and 8 percent get to work by other means of transportation. Suppose a sample of 200 Wyoming workers is selected at random. Let the random variable D represent the number of workers in the sample who get to work by driving alone. What is the expected value of D ? a. 8 b. 16 c. 22 d. 46 e. 154

e

An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in Group 1 will receive the current fertilizer, Fertilizer A, and the plants in Group 2 will receive a new fertilizer, Fertilizer B. All other growing conditions, including amount of sunlight and water, will be kept the same for the two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment? a. The two types of fertilizer b. The sunlight and amount of water c. The 10 plants in Group 1 d. The 10 plants in Group 2 e. The 20 plants in the two groups

e

Data were collected on two variables, x and y, to create a model to predict y from x. A scatterplot of the collected data revealed a curved pattern with a possible cubic relationship (y=ax3y=ax3, where aa is a constant) between the variables. Which of the following transformations would be most appropriate for creating linearity between the variables? a. Taking the cube of y B. Taking the cube root of y C. Taking the cube root of both y and x D. Taking the log of y E. Taking the log of both y and x

e

Eighteen individuals who use a particular form of social media were assigned a new user interface to use when logging in to their accounts. After using the new user interface for a week, each individual was asked to rate how easy or hard the new user interface was to use on a scale from 1 (extremely easy) to 9 (extremely hard). Which of the following correctly identifies why this is not a well-designed experiment? a. There was a lack of control because not all individuals in the study used login passwords of the same length. b. The individuals may not have been randomly selected. c. There was not enough replication because the individuals used the new user interface for only one week. d. There was a lack of control because not all individuals in the study use social media. e. The study was not comparative—only one treatment was used.

e

Joy Happiness Love Anger Total 6 to 8 28 20 40 18 106 9 to 11 61 25 80 60 226 Total 89 45 120 78 332 One student from the school will be selected at random. What is the probability that the student is in the age-group of 6 to 8 years given that the selected student responded joy? a. 89/332 b. 28/332 c. 28/106 d. 106/332 e. 28/89

e

Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven? a b c d e

e

Which of the following is a high leverage point with respect to the regression? a. (5,8) b. 20, 31 c. 27, 22 d. 30,60 e. 80,70

e

Work Military College Undecided Total High School A 99 49 138 63 349 High School B 62 26 156 54 298 High School C 83 31 124 71 309 Total 244 106 418 188 956 One senior from the high schools will be selected at random. What is the probability that the senior selected will not be from High School B given that the senior responded with a choice other than college? a. 156/418 b. 538/956 c. 262/418 d. 658/965 e. 396/538

e

x| y | 1. 3 2. 4 3. 7 4. 8 5. 12 The table shows several values of xx and their corresponding values of y. Which of the following is closest to the correlation between x and y? a. -.98 b. -.95 c. .2 d. .95 e. .98

e