Chapter 1
Chapter 2
Chapter 3
Chapter 6
Chapter 9 (Chi Squared)
100
Roger claims that the two statistics most likely to change greatly when an outlier is added to a small data set are the mean and the median. Is Roger’s claim correct?
No, only the mean is likely to change greatly.
100
A researcher is studying a group of field mice. The distribution of the weight of field mice is approximately normal with mean 25 grams and standard deviation 4 grams. Which of the following is closest to the proportion of field mice with a weight greater than 33 grams?
A. 0.023
B. 0.046
C. 0.954
D. 0.977
E. 1.000
A. 0.023
100
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. 0.71
B. 0.00
C. -0.14
D. -0.87
E. -1.00
D. -0.87
100
In a certain game, a fair die is rolled and a player gains 20 points if the die shows a "6." If the die does not show a "6," the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player?
A. A gain of about 1,700 points
B. A gain of about 583 points
C. A gain of about 83 points
D. A loss of about 250 points
E. A loss of about 300 points
C. A gain of about 83 points
100
How are the expected counts calculated when a chi-square goodness-of-fit test is conducted?
A. The expected counts are calculated by multiplying each proportion in the null hypothesis by 100.
B. The expected counts are calculated by multiplying each proportion in the alternative hypothesis by 100.
C. The values observed from the sample are the expected counts.
D. The expected counts are calculated by multiplying each proportion in the null hypothesis by the sample size.
E. The expected counts are calculated by multiplying each proportion in the alternative hypothesis by the sample size.
D. The expected counts are calculated by multiplying each proportion in the null hypothesis by the sample size.
200
An amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. The following boxplot shows the heights of a sample of people who entered the amusement park on one day.
Based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction?
what is 50%
200
At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?
A. 0.17
B. 0.25
C. 0.36
D. 0.83
E. 0.95
A. 0.17
200
Which of the following is the best description of a positive association between two variables?
A. The values will create a line when graphed on a scatterplot.
B. The values will create a line with positive slope when graphed on a scatterplot.
C. As the value of one of the variables increases, the value of the other variable tends to decrease.
D. As the value of one of the variables increases, the value of the other variable tends to increase.
E. All values of both variables are positive.
D. As the value of one of the variables increases, the value of the other variable tends to increase.
200
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
C. 22
200
A company claims it audits its employees’ transactions based on their job level. For entry-level positions, the company claims that 50 percent get a basic audit, 30 percent get an enhanced audit, and 20 percent get a complete audit. The company tests this hypothesis using a random sample and finds X^2 = 0.771 with a corresponding p–value of 0.68. Assuming conditions for inference were met, which of the following is the correct interpretation of the p–value?
A. There is a 68 percent chance of obtaining a chi-square value of at least 0.771.
B. There is a 68 percent chance that the company’s claim is correct.
C. If the null hypothesis were true, there would be a 68 percent chance that the company’s claim is correct.
D. If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of 0.771.
E. If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.
E. If the null hypothesis were true, there would be a 68 percent chance of obtaining a chi-square value of at least 0.771.
300
The following boxplot shows the typical gas mileage, in miles per gallon, for 20 different car models.
Based on the boxplot, the top 25 percent of the cars have a typical gas mileage of at least how many miles per gallon?
What is 35
300
A statistician at a metal manufacturing plant is sampling the thickness of metal plates. If an outlier occurs within a particular sample, the statistician must check the configuration of the machine. The distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. Based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine?
A. 19.3mm
B. 20.6mm
C. 12.1mm
D. 23.5mm
E. 24.9mm
B. 20.6
300
A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient?
A. 0.64
B. 0.60
C. 0.40
D. 0.36
E. 0.13
B. 0.60
300
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. 7.82
300
A X^2 goodness-of-fit test was used to test the hypothesis that students at a local university select majors in the same proportions as other universities in the state. A chi-square test statistic of X^2 = 45.6 was calculated with a corresponding p-value of 0.005. Which of the following is correct?
A. There is sufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
B. There is sufficient evidence to conclude that students at the local university select majors in the same proportions as do students in the rest of the state.
C. There is insufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
D. There is insufficient evidence to conclude that students at the local university select majors in the same proportions as do students in the rest of the state.
E. Students at the local university select majors in the same proportions as do students in the rest of the state.
A. There is sufficient evidence to conclude that students at the local university do not select majors in the same proportions as do students in the rest of the state.
400
In northwest Pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. The data are shown in the back-to-back stemplot below.
Based on the stemplot, which of the following statements is true?
A. The median age and the range of ages are both greater for female bears than for male bears.
B. The median age and the range of ages are both less for female bears than for male bears.
C. The median age is the same for female bears and male bears, and the range of ages is the same for female bears and male bears.
D. The median age is less for female bears than for male bears, and the range of ages is greater for female bears than for male bears.
E. The median age is greater for female bears than for male bears, and the range of ages is less for female bears than for male bears.
A. The median age and the range of ages are both greater for female bears than for male bears.
400
The following boxplot summarizes the heights of a sample of 100 trees growing on a tree farm.
Emily claims that a tree height of 43 inches is an outlier for the distribution. Based on the 1.5×IQR rule for outliers, is there evidence to support the claim?
A. Yes, because (max−Q3) is greater than (Q1−min).
B. Yes, because 43 is greater than (Q3+IQR).
C. Yes, because 43 is greater than (Q1−1.5×IQR).
D. No, because 43 is not greater than (Q3+1.5×IQR).
E. No, because 43 is greater than (Q1−1.5×IQR).
D. No, because 43 is not greater than (Q3+1.5×IQR).
400
For a specific species of fish in a pond, a wildlife biologist wants to build a regression equation to predict the weight of a fish based on its length. The biologist collects a random sample of this species of fish and finds that the lengths vary from 0.75 to 1.35 inches. The biologist uses the data from the sample to create a single linear regression model. Would it be appropriate to use this model to predict the weight of a fish of this species that is 3 inches long?
A. Yes, because 3 inches falls above the maximum value of lengths in the sample.
B. Yes, because the regression equation is based on a random sample.
C. Yes, because the association between length and weight is positive.
D. No, because 3 inches falls above the maximum value of lengths in the sample.
E. No, because there may not be any 3-inch fish of this species in the pond.
D. No, because 3 inches falls above the maximum value of lengths in the sample.
400
A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation of 10 pounds. If the weights of individual passengers are independent, what is the probability that a group of four adult male passengers will exceed the acceptable weight limit of 800 pounds?
A. 0.023
B. 0.046
C. 0.159
D. 0.317
E. 0.977
C. 0.159
400
Which of the following is a reason not to use a chi-square test of homogeneity to analyze a set of data?
A. The data consist of one categorical variable for two or more different populations and are summarized by counts in a two-way table.
B. The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.
C. The data were obtained from more than two populations to investigate whether the proportions for categorical data collected are the same.
D. The data were obtained from four different regions to investigate whether the distribution of a categorical variable is different across the four regions.
E. The data were obtained using a simple random sample of a population from last year and a simple random sample of the same population from this year where the data collected were categorical variables
B. The data were obtained through a simple random sample from a single population and summarized by counts on two categorical variables.
500
Data will be collected on the following variables. Which variable can be considered discrete?
A. The height of a person
B. The weight of a person
C. The length of a person’s arm span
D. The time it takes for a person to solve a puzzle
E. The number of books a person finished reading last month
E. The number of books a person finished reading last month
500
An amusement park attraction has a sign that indicates that a person must be at least 48 inches tall to ride the attraction. The following boxplot shows the heights of a sample of people who entered the amusement park on one day.
Based on the boxplot, approximately what percent of the people who entered the amusement park met the height requirement for the attraction?
50%
500
The following is a residual plot for a linear regression of y versus x.
What is indicated by the plot?
A. A linear model is appropriate.
B. A linear model is not appropriate.
C. Variability in y is constant for all values x.
D. At least one point is influential with respect to the regression.
E. At least one point is an outlier with respect to the regression.
B. A linear model is not appropriate.
500
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S 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 standard deviation 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. Mean 3 and standard deviation 5
500
A local restaurant claims that it gets 45 percent of its customers from Monday through Thursday, 20 percent on Friday, 20 percent on Saturday, and 15 percent on Sunday. How many degrees of freedom should be used to conduct a chi-square goodness-of-fit test of the claim?
A. 3
B. 4
C. 6
D. 7
E. It is not possible to determine the degrees of freedom without knowing the sample size.
A. 3