Unit 2 - Review 2

The following bar chart shows the number of different types of animals at two county fairs. Fair X had a total of 645 animals, and fair Y had a total of 590 animals. Which of the following statements is supported by the bar chart?

• The total number of cows, pigs, and horses combined is less at fair X than at fair Y.

• Fair X has at least 20 more chickens than fair Y.

• At fair X, the number of sheep is twice the number of horses.

• The percentage of all animals at fair Y that are goats is equal to the percentage of all animals at fair X that are goats.

• The percentage of all animals at fair Y that are goats is greater than the percentage of all animals at fair X that are goats.

The following table shows the number of registered voters in three different regions and the political party in which they are registered. Which of the following statements is supported by the table?

• The region with the greatest proportion of voters who are registered Democrat is region A.

• The region with the least proportion of voters who are registered Republican is region A.

• The region with the greatest proportion of voters who are registered Republican is region B.

• The proportion of voters who are registered Independent in region A is less than the proportion of voters who are registered Independent in region C.

• The proportion of voters who are registered Republican in region C is greater than the proportion of voters who are registered Republican in region B.

A recent study investigated whether renowned violinists were able to classify the age of a violin. In the study, violins constructed before 1900 and violins constructed after 2010 were used. The violinists played each violin and were asked to classify the violin as old (constructed before 1900) or new (constructed after 2010). The responses are shown in the following table. Which of the following statements is supported by the results in the table?

• The proportion of all new violins that are correctly classified is equal to the proportion of all old violins that are correctly classified.

• The proportion of all new violins that are incorrectly classified is equal to the proportion of all old violins that are correctly classified.

• The proportion of all incorrectly classified violins that are old is equal to the proportion of all correctly classified violins that are new.

• The proportion of all incorrectly classified violins that are new is equal to the proportion of all correctly classified violins that are new.

• The proportion of all correctly classified violins that are old is equal to the proportion of all new violins that are incorrectly classified.

The scatterplot below displays the relationship between the percent change in the population of wolves and the moose density, in number of moose per square kilometer, over a 19-year period in a certain region. Notice that the association is negative, and that the points seem to be more spread out at higher moose densities. Suppose the variables on the scatterplot were reversed, so that moose density was the response variable on the vertical axis, and percent change in wolf population was the explanatory variable on the horizontal axis. Which of the following would be true?

• The association would still be negative, but the strength of the association would increase.

• The association would be positive, and the strength of the association would increase.

• The association would still be negative, but the strength of the association would decrease.

• The association would be positive, but the strength of the association would not change.

• The direction and strength of the association would not change.

A food truck owner recorded the temperature at noon, in degrees Fahrenheit, and the number of bowls of soup sold during the lunch hour for a random sample of 5 days. The data are shown in the following table. The mean temperature of the sample is 62 degrees Fahrenheit, and the mean number sold is 14. What is the correlation between the temperature and the number sold?

• -0.85

• -0.68

• 0.68

• 0.73

• 0.85

A certain middle school opens at 7 A.M., and classes begin at 8 A.M. A sociologist gathered data on the number of minutes after 7 A.M. that a student arrives at school and the number of friends the student has on social media. The correlation between the two variables indicated a strong negative relationship. Which of the following is an appropriate interpretation of the correlation?

• Students who arrive early to school have more friends on social media

• Students who arrive late to school have more friends on social media.

• Having a lot of friends on social media causes a student to arrive late for school

• As the number of minutes of arriving after 7 A.M. increases, the number of friends on social media tends to increase.

• As the number of minutes of arriving after 7 A.M. increases, the number of friends on social media tends to decrease.

A grocery store wants to examine the relationship between the sales amounts each day at two different locations, store A and store B. The sales amount each day, in dollars, was recorded for 10 days at each store. The least-squares regression line is ŷ=−3,000+1.2x, where x represents the sales amounts each day at store A and y represents the sales amounts each day at store B. If the mean of the 10 sales amounts for store B is $45,000, what is the mean of the 10 sales amounts for store A?

• $35,000

• $40,000

• $42,000

• $45,000

• $51,000

The least-squares regression model ŷ=−3.4+5.2x and correlation coefficient r=0.66 were calculated for a set of bivariate data with variables x and y. Which of the following is closest to the proportion of the variation in y that cannot be explained by the explanatory variable?

• 81%

• 66%

• 56%

• 44%

• 34%

In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Which of the following statements is the best interpretation of the value 6.8 shown in the output?

• 
  ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP.

• 
  WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA.

• For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units.

• For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units.

• Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.