Test 3 MCAP Statistics Name

Test 3 MCAP Statistics Name:

Directions: Work on these sheets.

Part 1: Multiple Choice. Circle the letter corresponding to the best answer.

1.A regression of the amount of calories in a serving of breakfast cereal vs. the amount of fat gave the following results: Calories = 97.1053 + 9.6525(Fat). Which of the following is FALSE?

(a) It is estimated that for every additional gram of fat in the cereal, the number of calories

increases by about 10.

(b)It is estimated that in cereals with no fat, the total amount of calories is about 97.

(d)The correlation between amount of fat and calories is positive.

(e)One cereal has 140 calories and 5 g of fat. Its residual is about 5 cal.

3. A community college announces that the correlation between college entrance exam grades and scholastic achievement was found to be –1.08. On the basis of this you would tell the college that

(a)the entrance exam is a good predictor of success.

(b)the exam is a poor predictor of success.

(c)students who do best on this exam will be poor students.

(d)students at this school are underachieving.

(e)the college should hire a new statistician.

4.A researcher finds that the correlation between the personality traits “greed” and “superciliousness” when both are measured on a numerical scale is –0.40. What percent of the variation in greed can be explained by the relationship with superciliousness?

(a)0%(b) 16%(c) 20%(d) 40% (e) 60%

5.Scientists rated the activity level of fish at different temperatures (Celsius). A rating of 0 indicates no activity and a rating of 100 indicates extremely heavy activity. The data they collected are given in the table below.

Fish act. / 82 / 65 / 62 / 90 / 51 / 79 / 87
Water temp. / 21 / 24 / 29 / 18 / 29 / 22 / 20

Which of the following statements is true?

(a) The level of fish activity helps explain the water temperature. At low levels of fish activity, the water is cooler. As fish move around more, water temperature increases.

(b) Increasing the water temperature causes the fish to swim faster.

(d) The correlation coefficient, 0.91, indicates that there is a fairly strong positive linear relationship between level of fish activity and temperature.

(e) Based on our sample data, we can safely estimate that the level of fish activity would be about 34 at a temperature of 12.

7.A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give = 8.4, = 2.1, = 14.2, = 3.8, and r = 0.86. What is the slope of the least-squares regression line of number of service calls on number of copiers?

(a) 0.86

(b) 1.56

(d) None of these

(e) Can’t tell from the information given

8.“Normal” body temperature varies by time of day. A series of readings was taken of the body temperature of a subject. The mean reading was found to be 36.5°C with a standard deviation of 0.3°C. When converted to °F, the mean and standard deviation are (°F = °C(1.8) + 32):

(a)97.7, 32

(b)97.7, 0.30

(d)97.7, 0.97

(e)97.7, 1.80

9.If data set A of (x,y) data has correlation coefficient r = 0.65, and a second data set B has correlation r = –0.65, then

(a) the points in A exhibit a stronger linear association than B.

(b) the points in B exhibit a stronger linear association than A.

(d)you can’t tell which data set has a stronger linear association without seeing the data.

(e)a mistake has been made—r cannot be negative.

10.There is a linear relationship between the number of chirps made by the striped ground cricket and the air temperature. A least-squares fit of some data collected by a biologist gives the model

= 25.2 + 3.3x, 9 < x < 25, where x is the number of chirps per minute and is the estimated temperature in degrees Fahrenheit. What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?

(a)3.3°F(b) 16.5°F(c) 25.2°F (d) 28.5°F (e) 41.7°F

11.Which of the following relationships is most likely to result in a strong negative correlation?

(a)The number of people showering in a college dorm and the water pressure in each shower.

(b) The outdoor temperature and the number of fans running in non-air-conditioned dorm rooms.

(d) The price of a home and its square footage.

(e) The fuel efficiency of a car (miles per gallon) and its speed.

12.A set of data relates the amount of annual salary raise and the performance rating. The least

squares regression equation is = 1400 + 2000x where y is the raise amount and x is the performance rating. Which of statements (a) to (d) is not correct?

(a) For each increase of one point in performance rating, the raise will increase on average by $2000.

(b)This equation produces predicted raises with an average error of 0.

(c)A rating of 0 will yield a predicted raise of $1400.

(d)The correlation between salary raise and performance rating is positive.

(e)All of the above are true.

14.For children between the ages of 18 months and 29 months, there is approximately a linear relationship between height and age. The relationship can be represented by

= 64.93 + 0.63x, where y represents height (in centimeters) and x represents age (in months). Joseph is 22.5 months old and is 80 centimeters tall. What is Joseph's residual?

(a) 79.1 (b) 0.9 (c) 0.9 (d) 56.6 (e) 64.93

15.A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties A and B are represented by x’s and o’s, respectively, in the following scatterplot. Which of the following statements is FALSE?

(a) Considering Variety A only, there is a negative correlation between sepal length and width.

(b) Considering Variety B only, the least-squares regression line for predicting sepal length from sepal width has a negative slope.

(d) Considering each variety separately, there is a positive correlation between sepal length and width.

(e) Considering both varieties, the least-squares regression line for predicting sepal length from sepal width has a positive slope.

16.On May 11, 50 randomly selected subjects had their systolic blood pressure (SBP) recorded twice—the first time at about 9:00 a.m. and the second time at about 2:00 p.m. If one were to examine the relationship between the morning and afternoon readings, then one might expect the correlation to be

(a) near zero, as morning and afternoon readings should be independent.

(b) high and positive, as those with relatively high readings in the morning will tend to have relatively high readings in the afternoon.

(c) high and negative, as those with relatively high readings in the morning will tend to have relatively low readings in the afternoon.

(d) near zero, as correlation measures the strength of the linear association.

(e) near zero, as blood pressure readings should follow approximately a Normal distribution.

18. Many professional schools require applicants to take a standardized test. Suppose that 1000

students take the test, and you find that your mark of 63 (out of 100) is the 73rd percentile.

This means that

(a)at least 73% of the people scored 63 or better.

(b)at least 270 people scored 73 or better.

(c)at least 730 people scored73 or better.

(d)at least 27% of the people scored 73 or worse.

(e)at least 270 people scored 63 or better.

19.Mr. Nerdly asked the students in his AP Statistics class to report their overall grade point averages and their SAT Math scores. The scatterplot below provides information about his students’ data. The dark line is the least-squares regression line for the data, and its equation is .

Which of the following statements about the highlighted point is FALSE?

(a) This student has a grade point average of 2.9 and an SAT Math score of 670.

(b) If we used the least-squares line to predict this student’s SAT Math score, we would make a prediction that is too low.

(d) Removing this data point would cause the correlation coefficient to increase.

(e) Removing this student’s data point would increase the slope of the least-squares line.

Chapter 31Test 3B