Quiz 2

Question 1

A teacher gave a 25‑question multiple‑choice test. After scoring the tests, she computed a mean and standard deviation of the scores. The standard deviation was 0. Based on this information:

a. the teacher must have made a mistake in her computations.
b. all of the students had the same score.
c. about half of the scores were above the mean.

Answer 1

b.all of the students had the same score.

Question 2

Does the value of the standard deviation depend on the value of the mean?

a. No, because the center of a distribution and the spread are not related.
b. Yes, because if the mean gets larger, the standard deviation will also get larger.
c. Yes, because the mean must be known in order to calculate the standard deviation.

Answer 2

c.Yes, because the mean must be known in order to calculate the standard deviation.

Question 3

A sample was taken of the salaries of four employees from a large company. The following are their salaries, in thousands of dollars, for this year.

33 31 24 36

The variance of their salaries is:

a. 26
b. 5.1.
c. 31

Answer 3

a. 26

Question 4

Enteroliths are calcifications that form in the gut of a horse. The stones can cause considerable morbidity and mortality. A study was conducted to investigate the factors (such as diet and environment) that may be related to the formation of enteroliths. The study contained seven stallions; their ages (in years) are as follows:

10 20 4 13 21 16 16
The mean age for this group of stallions is:

a. 16
b. 12.5
c. 14.3
d. 13

Answer 4

c. 14.3

Question 5

Which of the following sets of four numbers has the smallest standard deviation?

a. 5,5,5,6
b. 7,8,9,10
c. 0,0,10,10
d. 0,1,2,3

Answer 5

a. 5,5,5,6

Question 6

The given graph represents a population with a Normal distribution.

The normal distribution graph represents 6 segments from which 5 segments are shaded and the first segment from the left is not shaded. The shaded area represents the proportion that lies at or above 2 standard deviations below the mean.

Approximately what percent of the population is represented by the shaded area?

a. 99.7%
b. 95%
c. 99.85%
d. 97.5%

Answer 6

d. 97.5%

Question 7

An instructor in a large lecture class found, at the end of the semester, that the total point distribution in his class was approximately Normal, with a mean of 530 and a standard deviation of 80. About what percent of students will score between 370 and 690?

a. 68%
b. 99.7%
c. 95%

Answer 7

c. 95%

Question 8

You recently took a statistics exam in a large class. The instructor tells the class that the scores were Normally distributed, with a mean of 72 (out of 100 ) and a standard deviation of 12 . The median for the exam is:

a. 60 .
b. 72 .
c. 50 .
d. 84 .

Answer 8

b. 72 .

Question 9

Your friend took an introductory statistics class last year and learned all about density curves. He draws a smooth curve with a long left tail. For such a curve, which of the following is true for the mean and median?

a. mean > median
b. There is not enough information to determine any of the answer options.
c. mean < median
d. mean = median

Answer 9

c. mean < median

Question 10

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper’s family and their grocery bill for that week. The response variable is:

a. weekly income.
b. None of the answer options is correct.
c. weekly expenditure.
d. gender.

Answer 10

c. weekly expenditure.

Question 11

Consider the following scatterplot of two variables 𝑥 and 𝑦 .

The scatterplot shows the correlation between x and y. The x-axis ranges from 1.0 to 3.0 with increments of 0.5. The y-axis ranges from 0.0 to 1.0 with increments of 0.2. The scatter plot does not show a linear relationship. The dots are marked in

We may conclude:

a. the correlation between 𝑥 and 𝑦 must be close to 1 , because there is a nearly perfect relation between them.
b. the correlation between 𝑥 and 𝑦 could be any number between –1 and +1 ; we can say nothing more without knowing the actual values.
c. the correlation between 𝑥 and 𝑦 is close to 0 because, although there is a strong relationship between these variables, it isn’t a linear relationship.
d. the correlation between 𝑥 and 𝑦 must be close to –1 , because there is a nearly perfect relation between them but it is not a straight line relation.

Answer 11

c. the correlation between 𝑥 and 𝑦 is close to 0 because, although there is a strong relationship between these variables, it isn’t a linear relationship.

Question 12

For each menu item at a fast food restaurant, the fat content (in grams) and the number of calories were recorded. A scatterplot of these data is given:

The scatterplot shows the correlation between fat content and the number of calories.

The restaurant decides to add six new high-calorie, low-fat pasta dishes to its menu. What is a plausible value for the new correlation coefficient describing the relationship between fat and calories?

a. –0.2
b. –0.7
c. +0.7
d. +0.2

Answer 12

c. +0.7

Question 13

A researcher states that bone density in women is negatively associated with age. This means that:

a. as women get older, bone density tends to decrease.
b. older women aren’t any more likely than younger women to have below-average bone density.
c. below-average values of age tend to accompany below-average values of bone density.
d. as women get older, bone density tends to increase.

Answer 13

a. as women get older, bone density tends to decrease.

Question 14

The graph below shows a scatterplot of midterm scores plotted against homework scores. The graph contains several points that correspond to unusually low homework scores, and one of those scores is associated with the highest midterm score.

The scatter plot shows midterm scores plotted against homework scores. The homework score is labeled on the horizontal axis, which ranges from 40 to 100 in increments of 10. The Midterm score is labeled on the vertical axis, which ranges from 500 to 900 in increments of 100. The dots presenting the relationship in the plot show a positive association between the homework and midterm scores. Few dots show low homework scores but associated with high midterm scores.

Removing this point will:

a. increase the correlation.
b. The effect cannot be determined from the scatterplot.
c. leave the correlation unchanged.
d. decrease the correlation.

Answer 14

a. increase the correlation.

Question 15

Archaeologists often find only parts of ancient human remains. For example, they may find a small finger bone, called the metacarpal bone. Is it possible to predict the height of a human from the length of a metacarpal bone? To investigate, a researcher measures the heights and metacarpal lengths of 200 adults. In making the scatterplot, the researcher should:

a. first determine if the heights of humans follow a Normal distribution.
b. plot the metacarpal length on the horizontal axis.
c. use a plotting scale that makes the overall trend roughly linear.
d. plot the height of the person on the horizontal axis.

Answer 15

b. plot the metacarpal length on the horizontal axis.

Question 16

A scatterplot can be used to illustrate the relationship between:

a. two quantitative variables.
b. All of the answer options are correct.
c. two categorical variables.
d. one categorical variable and one quantitative variable.

Answer 16

a. two quantitative variables.

Question 17

A scatterplot of the amount of alcohol consumed according to a food diary (DR) against the amount of alcohol consumed on a frequent food questionnaire (FFQ):

a. All of the answer options are correct.
b. shows the relationship between the answers from the DR and the FFQ.
c. assesses whether the relationship between the answers on the DR and the FFQ is positive.
d. shows the answers each study participant gave on the FFQ and the DR.

Answer 17

a. All of the answer options are correct.

Question 18

The volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is exercising (running on a treadmill) were both measured for 50 subjects. The goal is to determine if the volume of oxygen consumed during aerobic exercise can be estimated from the amount consumed at rest. The results are plotted below.

The scatterplot shows the volume of oxygen consumed (in liters per minute) while a person is at rest and while a person is running. The volume consumed at rest is located on the horizontal axis, which ranges from 0.1 to 0.7 with increments of 0.1. The volume consumed while running located on the vertical axis, which ranges from 1.5 to 5.5 with increments of 0.5. The dots available under plot show a positive association between the volume of oxygen consumed at rest and while running. Most of the reading points lie between 0.2 and 0.55 horizontal axis values, and between 1.6 and 5.0 vertical axis values. An outlier reading point is presented with horizontal and vertical axis coordinates 0.65 and 2.4, respectively.

In this study, the explanatory variable is:

a. the instrument used to measure the volume of oxygen consumed.
b. the volume of oxygen consumed while running.
c. either variable—it doesn’t matter which is considered the response.
d. the volume of oxygen consumed at rest.

Answer 18

d. the volume of oxygen consumed at rest.

Question 19

A researcher measures the correlation between two variables. This correlation tells us:

a. whether there is a relation between two variables.
b. whether a scatterplot shows an interesting pattern.
c. whether a cause-and-effect relation exists between two variables.
d. the strength and direction of a linear association between two variables.

Answer 19

d. the strength and direction of a linear association between two variables.