# Expert Answers

Question 1

A particularly common question in the study of wildlife behavior involves observing contests between 'residents' of a particular area and 'intruders.' In each contest, the 'residents' either win or lose the encounter (assuming there are no ties). Observers might record several variables, listed below. Which of these variables is categorical?

Question 1 options:

The duration of the contest (in seconds).

The number of animals involved in the contest.

Whether the 'residents' win or lose.

The total number of contests won by the 'residents.'

Question 2

The following is the number of minutes to commute from home to work

for a sample of automobile executives.

74 , 76 , 76 , 39 , 77 , 64 , 48 , 64 , 74 , 58 , 62 ,

30 , 49 , 66 , 41 , 68 , 39 , 32 , 55 , 38 ,

34 , 62 , 73 , 70 , 41 , 73 , 78 , 70 , 40 , 37

Find the mean of the sample.

Question 3

Find the median, range, and standard deviation of the sample in Question 2.

Question 4

Make and submit a frequency distribution of the sample in Question 2 using six

classes. Include class limits, midpoints, frequencies, relative

frequencies, and cumulative frequencies.

Describe the shape of the distribution as symmetric, uniform, right

skewed, or left skewed.

Question 5

For the histogram below, which of the following is true?

Question 5 options:

The mean is much larger than the median.

The mean is much smaller than the median.

The mean and median are approximately equal.

It is impossible to compare the mean and median for these data.

Question 6

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

What proportion of the population has scores below 26 on the Chapin test?

Question 6 options:

0.0139

0.0359

0.0808

0.1587

0.2743

0.4207

0.5793

Question 7

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

What proportion of the population has scores above 32 on the Chapin test?

Question 7 options:

0.0359

0.0808

0.1587

0.2743

0.4207

0.5793

Save

Question 8

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

How high a score must you have in order to be in the top 15% of the population in social insight?

Question 8 options:

27.62

28.37

29.21

30.18

31.41

33.22

34.40

36.63

Question 9 (7 points)

The household income in a certain community is normally distributed with a mean of $42,000 and a standard deviation of $5,000. The proportion of households with incomes between $44,000 and $50,000 is

Question 9 options:

0.290

0.445

0.600

0.733

0.157

Question 10 (7 points)

Which of the following statements is true?

Question 10 options:

The correlation coefficient equals the proportion of times two variables lie on a straight line.

The correlation coefficient will be +1.0 only if all the data lie on a perfectly horizontal straight line.

The correlation coefficient measures the fraction of outliers that appear in a scatter plot.

The correlation coefficient is a unit less number and must always lie between -1.0 and +1.0, inclusive.

Save

Question 11 (7 points)

Consider the following scatter plot.

The correlation between X and Y is approximately

Question 11 options:

-0.999

- 0.8

0.0

0.8

0.999

Save

Question 12 (7 points)

A college newspaper interviews a psychologist about a proposed system for rating the teaching ability of faculty members. The psychologist says, "The evidence indicates that the correlation between a faculty member's research productivity and teaching rating is close to zero."

A correct interpretation of this statement would be

Question 12 options:

good researchers tend to be poor teachers and vice versa

good teachers tend to be poor researchers and vice versa

good researchers are just as likely to be good teachers as they are bad teachers. Likewise for poor researchers.

good research and good teaching go hand in hand

Save

Question 13 (7 points)

In a statistics course a linear regression equation was computed to predict the final exam score from the score on the first test. The equation of the least-square regression line was

y=10+0.9x

where y represents the final exam score and x is the score on the first exam.

Suppose Joe scores a 78 on the first exam. What would be the predicted value of his score on the final exam?

Question 14

The number of people living on American farms has declined steadily during the past century. Here are data on the farm population (millions of persons) from 1935 to 1980:

Year 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

Population 32.1 30.5 24.4 23.0 19.1 15.6 12.4 9.7 8.9 7.2

Find the least squares regression equation of farm population on year. Hint: Use a computer or a graphing calculator to find equation.

Question 14 options:

Population = 969.5 - 0.484*Year

Population = 1055 - 0.529*Year

Population = 1167 - 0.587*Year

Population = 1204 - 0.606*Year

Population = 1689 - 0.766*Year

Question 15

A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their beginning salary is y = –2570.8 + 2.12x.

The current salaries had a mean of $32,070 with a standard deviation of $15,300. The beginning salaries had a mean of $16,340 with a standard deviation of $ 6202. What is the correlation between current and beginning salary?

A particularly common question in the study of wildlife behavior involves observing contests between 'residents' of a particular area and 'intruders.' In each contest, the 'residents' either win or lose the encounter (assuming there are no ties). Observers might record several variables, listed below. Which of these variables is categorical?

Question 1 options:

The duration of the contest (in seconds).

The number of animals involved in the contest.

Whether the 'residents' win or lose.

The total number of contests won by the 'residents.'

Question 2

The following is the number of minutes to commute from home to work

for a sample of automobile executives.

74 , 76 , 76 , 39 , 77 , 64 , 48 , 64 , 74 , 58 , 62 ,

30 , 49 , 66 , 41 , 68 , 39 , 32 , 55 , 38 ,

34 , 62 , 73 , 70 , 41 , 73 , 78 , 70 , 40 , 37

Find the mean of the sample.

Question 3

Find the median, range, and standard deviation of the sample in Question 2.

Question 4

Make and submit a frequency distribution of the sample in Question 2 using six

classes. Include class limits, midpoints, frequencies, relative

frequencies, and cumulative frequencies.

Describe the shape of the distribution as symmetric, uniform, right

skewed, or left skewed.

Question 5

For the histogram below, which of the following is true?

Question 5 options:

The mean is much larger than the median.

The mean is much smaller than the median.

The mean and median are approximately equal.

It is impossible to compare the mean and median for these data.

Question 6

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

What proportion of the population has scores below 26 on the Chapin test?

Question 6 options:

0.0139

0.0359

0.0808

0.1587

0.2743

0.4207

0.5793

Question 7

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

What proportion of the population has scores above 32 on the Chapin test?

Question 7 options:

0.0359

0.0808

0.1587

0.2743

0.4207

0.5793

Save

Question 8

The Chapin Social Insight Test evaluates how accurately the subject appraises other people. In the reference population used to develop the test, scores are approximately normally distributed with mean 25 and standard deviation 5. The range of the possible scores is 0 to 41.

How high a score must you have in order to be in the top 15% of the population in social insight?

Question 8 options:

27.62

28.37

29.21

30.18

31.41

33.22

34.40

36.63

Question 9 (7 points)

The household income in a certain community is normally distributed with a mean of $42,000 and a standard deviation of $5,000. The proportion of households with incomes between $44,000 and $50,000 is

Question 9 options:

0.290

0.445

0.600

0.733

0.157

Question 10 (7 points)

Which of the following statements is true?

Question 10 options:

The correlation coefficient equals the proportion of times two variables lie on a straight line.

The correlation coefficient will be +1.0 only if all the data lie on a perfectly horizontal straight line.

The correlation coefficient measures the fraction of outliers that appear in a scatter plot.

The correlation coefficient is a unit less number and must always lie between -1.0 and +1.0, inclusive.

Save

Question 11 (7 points)

Consider the following scatter plot.

The correlation between X and Y is approximately

Question 11 options:

-0.999

- 0.8

0.0

0.8

0.999

Save

Question 12 (7 points)

A college newspaper interviews a psychologist about a proposed system for rating the teaching ability of faculty members. The psychologist says, "The evidence indicates that the correlation between a faculty member's research productivity and teaching rating is close to zero."

A correct interpretation of this statement would be

Question 12 options:

good researchers tend to be poor teachers and vice versa

good teachers tend to be poor researchers and vice versa

good researchers are just as likely to be good teachers as they are bad teachers. Likewise for poor researchers.

good research and good teaching go hand in hand

Save

Question 13 (7 points)

In a statistics course a linear regression equation was computed to predict the final exam score from the score on the first test. The equation of the least-square regression line was

y=10+0.9x

where y represents the final exam score and x is the score on the first exam.

Suppose Joe scores a 78 on the first exam. What would be the predicted value of his score on the final exam?

Question 14

The number of people living on American farms has declined steadily during the past century. Here are data on the farm population (millions of persons) from 1935 to 1980:

Year 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980

Population 32.1 30.5 24.4 23.0 19.1 15.6 12.4 9.7 8.9 7.2

Find the least squares regression equation of farm population on year. Hint: Use a computer or a graphing calculator to find equation.

Question 14 options:

Population = 969.5 - 0.484*Year

Population = 1055 - 0.529*Year

Population = 1167 - 0.587*Year

Population = 1204 - 0.606*Year

Population = 1689 - 0.766*Year

Question 15

A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their beginning salary is y = –2570.8 + 2.12x.

The current salaries had a mean of $32,070 with a standard deviation of $15,300. The beginning salaries had a mean of $16,340 with a standard deviation of $ 6202. What is the correlation between current and beginning salary?

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