Advanced Placement Statistics Test: Can You Pass? Trivia Quiz

1. Since many individuals walk around their homes in their socks, a manufacturer has created a material for socks that are believed to be more resistant to wear than cotton. The manufacturer wishes to test this belief over a period of a month. Given a group of volunteers, which of the following designs will best test this new material's resistance to wear?

Have the volunteers wear the socks made from the new material for a month, and check the wear on the socks at the end of the month.

Allow half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month.

Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. Compare the wear on the socks at the end of the month.

Randomly assign half of the volunteers to wear cotton socks, while the other half wear socks made of the new material. At the end of two weeks, the volunteers should change sock types. Compare the wear on the socks at the end of the month.

For each volunteer, randomly choose which foot wears a cotton sock, while the other foot wears a sock made of the new material. Compare the wear on the socks at the end of the month.

The best design to test the new material's resistance to wear is to randomly assign each volunteer to wear a cotton sock on one foot and a sock made of the new material on the other foot. This design allows for a direct comparison between the two types of socks on the same individual, eliminating any potential individual differences in wear patterns. By comparing the wear on the socks at the end of the month, the manufacturer can determine which material is more resistant to wear.

Explanation

The best design to test the new material's resistance to wear is to randomly assign each volunteer to wear a cotton sock on one foot and a sock made of the new material on the other foot. This design allows for a direct comparison between the two types of socks on the same individual, eliminating any potential individual differences in wear patterns. By comparing the wear on the socks at the end of the month, the manufacturer can determine which material is more resistant to wear.

2. Suppose we have a random variable X as shown below. What is the mean of X?

0.29

0.71

4.35

10.65

None of the above.

The mean of a random variable is a measure of central tendency that represents the average value of the variable. In this case, the mean of X is 4.35.

Explanation

The mean of a random variable is a measure of central tendency that represents the average value of the variable. In this case, the mean of X is 4.35.

3. Which of the following statements about the correlation coefficient are true? (I). The correlation coefficient and the slope of the regression line may have opposite signs. (II). A correlation of 1 indicates a perfect cause-and-effect relationship between the variables. (III). Correlations of +.87 and −.87 indicate the same degree of clustering around the regression line.

I only

II only

III only

I and II

I, II, and III

The correlation coefficient measures the strength and direction of the linear relationship between two variables. Statement (I) is true because the correlation coefficient and the slope of the regression line can have opposite signs if the relationship is negative. Statement (II) is false because a correlation of 1 indicates a perfect positive linear relationship, not a cause-and-effect relationship. Statement (III) is true because correlations of +.87 and -.87 indicate the same degree of clustering around the regression line, just in opposite directions.

Explanation

The correlation coefficient measures the strength and direction of the linear relationship between two variables. Statement (I) is true because the correlation coefficient and the slope of the regression line can have opposite signs if the relationship is negative. Statement (II) is false because a correlation of 1 indicates a perfect positive linear relationship, not a cause-and-effect relationship. Statement (III) is true because correlations of +.87 and -.87 indicate the same degree of clustering around the regression line, just in opposite directions.

4. The graph shows cumulative proportions plotted against land values (in dollars per acre) for farms on sale in a rural community. What is the approximate median land value?

$2000

$2250

$2500

$2750

$3000

The approximate median land value can be determined by finding the value that corresponds to the point on the graph where the cumulative proportion is closest to 0.5. In this case, it appears that the cumulative proportion is closest to 0.5 at a land value of $2000. Therefore, the approximate median land value is $2000.

Explanation

The approximate median land value can be determined by finding the value that corresponds to the point on the graph where the cumulative proportion is closest to 0.5. In this case, it appears that the cumulative proportion is closest to 0.5 at a land value of $2000. Therefore, the approximate median land value is $2000.

5. Following is a histogram of ages of people applying for a particular high-school teaching position. Which of the following statements are true? (I). The median age is between 24 and 25. (II). The mean age is between 22 and 23. (III). The mean age is greater than the median age.

I only

II only

III only

All are true.

None are true.

The histogram shows that the distribution of ages is skewed to the right, indicating that there are more younger applicants. This means that the median age will be less than the mean age. Therefore, statement III is true. However, there is no information provided to determine whether statement I or statement II is true. Therefore, only statement III is true.

Explanation

The histogram shows that the distribution of ages is skewed to the right, indicating that there are more younger applicants. This means that the median age will be less than the mean age. Therefore, statement III is true. However, there is no information provided to determine whether statement I or statement II is true. Therefore, only statement III is true.