Statistics Diagnostic

A college professor conducted a survey in order to assess how much money nursing majors spend on course material compared to all other majors. To do so, she selected a random sample of 34 students. Each student was classified as a nursing major or as a non-nursing major. They were then asked how much they spent on books and other materials required for their courses this semester. Shown above are parallel boxplots summarizing the responses. Based upon the boxplots, which of the following statements cannot be concluded?

• The range of the distribution of the cost of course materials for nursing majors is about the same as that of non-nursing majors.

• The maximum cost for non-nursing majors is greater than the median cost for nursing majors.

• The variability of the cost of course materials for the middle 50% of nursing majors is greater than the variability of the middle 50% for non-nursing majors.

• The median cost of course materials for nursing majors is over $300 more than the median cost of course materials for non-nursing majors.

• The boxplots reveal that 17 students are nursing majors and 17 students are non-nursing majors.

In order to compare the real estate markets in Pittsburgh and Philadelphia, a realtor selected a random sample of 150 homes in the Pittsburgh area and 100 homes in the Philadelphia area. Shown above are dotplots showing the distribution of home price for the homes in these two cities. The mean home price for both cities is approximately $500,000. The standard deviation of home price for one city is $100,740 and the other is $267,210. Which of the following gives the correct value and interpretation of the standard deviation of the home prices for homes in the Pittsburgh area?

• The price of homes in the Pittsburgh sample are within $100,740 of the mean home price of $500,000.

• In the sample of homes from Pittsburgh, most of the home prices are at least $100,740 above or below the mean home price of $500,000

• The price of the homes in the Pittsburgh sample typically vary by about $267,210 from the mean home price of $500,000.

• In the sample of homes from Pittsburgh, the middle 50% of home prices are within $267,210 of the mean home price of $500,000.

• The price of homes in the Pittsburgh sample are $100,740 from the mean home price of $500,000

The segmented bar graph shows how many of the first 44 United States Presidents have died while in office, classified by political party. What proportion of these Presidents have died while in office?

• 0.045

• 0.080

• 0.091

• 0.182

• 0.662

A grocery store manager wants to estimate the mean purchase total for all customers that shop at her store. To do so, she selects a random sample of 30 receipts from the large list of all receipts that are stored in the computer. Shown above is a dotplot of the results. The mean purchase total is $93.80 and the median purchase total is $75.80. The store manager investigates and learns that the customer that made a $500 purchase had not purchased groceries, but rather a $500 gift card. Because this customer’s purchase was not typical, the manager decides to exclude this total from the data set. How will removing the $500 purchase from the data set affect the value of the mean and the median?

• The mean will decrease more than the median.

• The mean will decrease less than the median

• The mean will stay the same, but the median will decrease

• The mean will increase more than the median.

• The mean will increase, but not as much as the median.

When homeowners list their home for sale, they begin by listing it for a price that is greater than what they expect to receive. The longer a home is on the market, without being sold, the more the price drops. A realtor selects 50 homes that are currently listed for sale. A scatterplot reveals that the association between x = the number of days the home is on the market and y = the current asking price ($) is fairly linear and can be modeled by the equation shown above. Additionally, 85.4% of the variation in the current asking price can be explained by this linear model. Which of the following is the value of the correlation (r) for the relationship between x and y?

• –200

• –0.924

• 0.146

• 0.854

• 0.924

Active is an energy drink that claims to provide physical strength. To test this claim, the producers of Active conducted a study. The company recruited 25 high school athletes and 4 professional football players to participate in the study. The high school athletes were each randomly assigned to drink between 1 and 5 ounces of Active. The professional football players were assigned to drink either 30 or 31 ounces. After waiting 10 minutes they completed as many pull-ups as they could. Shown above is a scatterplot showing the number of energy drinks consumed and the number of pull ups that were completed by each participant, as well as a line of best fit. Which of the following would increase if the professional football players were removed from the data set?

• r

• r²

• the slope

• the standard deviation of the residuals

• none of the above

Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Shown above is computer output showing the regression analysis. Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading.

• Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.

• Slope = 0.0457. The predicted distance the drivers were able to drive increases by 0.0457 miles for each additional mile reported by the gauge.

• Slope = –0.7928. The predicted distance the drivers were able to drive decreases by 0.7928 miles for each additional mile reported by the gauge.

• Slope = 1.1889. For each additional mile reported by the gauge, the drivers were able to drive an additional 1.1889 miles.

• Slope = 0.0457. For each additional mile reported by the gauge, the drivers were able to drive an additional 0.0457 miles.

A well-balanced stock market portfolio will often experience an exponential growth. A particular investor with a well-balanced stock market portfolio records the portfolio balance every month, in thousands of dollars, from the date of investment. The roughly exponential growth can be transformed to a linear model by plotting the natural log of the balances versus time, in months, where t = 0 represents the date the money was invested. The linear regression equation for the transformed data is shown above. Using this equation, what is the predicted balance of the portfolio after 2 years (24 months)?

• $5,654

• $6,798

• $285,431

• $896,053

• $948,464

At Central High School, 28% of the students are Freshmen, 26% are Sophomores, 24% are Juniors, and 22% are Seniors. The student manager of the school newspaper would like to conduct a survey to estimate the proportion of each class that plans to attend the upcoming Football game. She suggests surveying a random sample of 100 students, but specifically by selecting random samples of 28 Freshmen, 26 Sophomores, 24 Juniors, and 22 Seniors. Which of the following is a true statement about this sampling procedure?

• This is a simple random sample because students of every class have an equal chance of being selected.

• This is a cluster random sample because there are 4 groups of students that are to be selected.

• This is a convenience sample because only 100 students are surveyed, which is a manageable size.

• This is a stratified random sample because a separate random sample is selected from each class

• This is a systematic random sample because each class makes up approximately one-fourth of the student body

A study is conducted to investigate whether customer satisfaction is greater among computer companies that offer tech support versus those that do not offer tech support. A random sample of 50 customers are selected from among those that purchased computers that offer tech support. A separate random sample of 40 customers are selected from among those that purchased computers that do not offer tech support. The study found that the mean satisfaction rating was significantly greater among customers that purchased computers that offer tech support. Which of the following is the best description of this study?

• An experiment using a completely randomized design.

• An experiment using a randomized block design.

• An experiment using a matched pairs design.

• An observational study using a simple random sample.

• An observational study using a stratified sample