Ch. 3 After School Review Session

Ch. 3 After School Review Session

1.The correlation between two scores X and Y equals 0.8. If both the X scores and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be

(A) -0.8

(B) -0.2

(C) 0.0

(D) 0.2

(E) 0.8

2.A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least squares regression line is , where x is the number of degrees Fahrenheit by which the temperature exceeds 50º. Which of the following best describes the meaning of the slope of the least squares regression line?

(A) For each increase in temperature of 1º F, the estimated number of chirps per minute increases by 10.53.

(B) For each increase in temperature of 1º F, the estimated number of chirps per minute increases by 3.41.

(C) For each increase of one chirp per minute, there is an estimated increase in temperature of 10.53º F.

(D) For each increase of one chirp per minute, there is an estimated increase in temperature of 3.41º F.

(E) The slope has no meaning because the units of measure for x and y are not the same.

3.Each of 100 laboratory rats has available both plain water and a mixture of water and caffeine in their cages. After 24 hours, two measures were recorded for each rat: the amount of caffeine the rat consume, X, and the rat’s blood pressure, Y. The correlation between X and Y was 0.428. Which of the following conclusions is justified on the basis of this study?

(A) The correlation between X and Y in the population of rats is also 0.428.

(B) If the rats stop drinking the water/caffeine mixture, this would cause a reduction in their blood pressure.

(C) About 18 percent of the variation in blood pressure can explained by a linear relationship between blood pressure and caffeine consumed.

(D) Rats with lower blood pressure do not like the water/caffeine mixture as much as do rats with higher blood pressure.

(E) Since the correlation is not very high, the relationship between the amount of caffeine consumed and blood pressure is not linear.

4.A delivery service places packages into large containers before flying them across the country. These filled containers vary greatly in their weight. Suppose the delivery service's airplanes always transport two such containers on each flight. The two containers are chosen so their combined weight is close to, but does not exceed, a specified weight limit. A random sample of flights with these containers is taken, and the weight of each of the two containers on each selected flight is recorded. The weights of the two containers on the same flight

(A)will have a correlation of 0

(B)will have a negative correlation

(C)will have a positive correlation that is less than 1

(D)will have a correlation of 1

(E) cannot be determined from the information given

5.In a recent survey, high school students and their parents were asked to rate 60 recently released movies. The ratings were on a scale from 1 to 9, where 1 was “horrible” and 9 was “excellent”. For each movie, the average rating by the students and the average rating by their parents was calculated and the scatterplot below was constructed. The horizontal axis represents the student rating, and the vertical axis represents the parent rating. Thus, an individual data point would represent the rating of a single movie.

Which of the following statements is justified by the scatterplot?

(A) The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give higher scores.

(B) The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give lower scores.

(C) The movies that the students liked the best also tended to be the movies that the parents liked the best, but the students tended to give higher scores.

(D) The movies that the students liked the best tended to be the movies that the parents liked the least, but the students tended to give lower scores.

(E) The movies that the students liked the best also tended to be the movies that the parents liked the best, but each group tended to give the same scores.

6.

Answers:

1. E
2. B
3. C
4. B
5. C
6. (a)Yes. (Hint: look at the scatter plot or residual plot.)

(b)$53.75

(c)96.7% of the variation in fuel consumption is explained by its linear relationship with number of cars.

(d)No. The data do not contain any information about fuel consumption for any trains with more than 50 cars. Using the LSRL to make prediction for 65 cars is extrapolation and therefore not reasonable.