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?

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.

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.

Advanced Placement Statistics Test: Can You Pass? Trivia Quiz

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1/5 Questions

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.

About This Quiz

Below is a trivia on Advanced Placement Statistics Test, Can You Pass? It is perfect for students taking statistics and is looking to see just how much they have understood from their classes. Are you among these students? Take up the quiz and get to see how much work you need to put into your studies. All the best!

Advanced Placement Statistics Test: Can You Pass? Trivia Quiz - Quiz

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.
Correct Answer

A. 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.

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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
Correct Answer

A. III only

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.

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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
Correct Answer

A. $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.

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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.
Correct Answer

A. III only

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.

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Advanced Placement Statistics Test: Can You Pass? Trivia Quiz

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

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?

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.