Statistics — Test Answers

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1
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Which of the following statements best describes the distribution?

A
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
B
The distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
C
The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. There are no outliers.
D
The distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.
2
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Which statement must be true?

A
Each distribution has the same mean and a different standard deviation.
B
Each distribution has a different mean and the same standard deviation.
C
Each distribution has the same mean and the same standard deviation.
D
Each distribution has a different mean and a different standard deviation.
3

Which of the following statements best describes the dotplot?

A
The distribution of quiz scores is unimodal symmetric with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
B
The distribution of quiz scores is skewed left with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
C
The distribution of quiz scores is unimodal symmetric with a center around 26 and varies from 20 to 30. There are possible outliers at 12, 14, 15, and 16.
D
The distribution of quiz scores is skewed right with a center around 24 and varies from 12 to 30. There are possible outliers at 12, 14, 15, and 16.
6

When making a statistical inference about the mean of a normally distributed population based on a sample drawn from that population, which of the following statements is correct, all else being equal?

A
The 90 percent confidence interval is narrower than the 95 percent confidence interval.
B
The 68 percent confidence interval is wider than the 90 percent confidence interval.
C
The 99 percent confidence interval is narrower than the 68 percent confidence interval.
D
The 90 percent confidence interval is wider than the 99 percent confidence interval.
9

Which normal distribution has the greatest standard deviation?

A
Image with description Number line with values from 40 to 80 and a bell-shaped curve above it. The curve reaches its highest point near 60 and decreases symmetrically toward both sides, approaching the horizontal axis near 40 and 80. The graph represents a normal distribution centered at 60.
B
Image with description Number line labeled from negative 8 to 32. A smooth bell-shaped curve rises from near the number line at the left, reaches a maximum near 16, and then decreases symmetrically toward the right, approaching the number line again near 40. The distribution is centered at 16.
C
Image with description Number line labeled from 16 to 56 with a narrow bell-shaped curve above it. The curve reaches its highest point near 32 and decreases rapidly on both sides, approaching the number line near 24 and 40. The distribution is symmetric about 32 and has a smaller spread than a typical bell curve.
D
Image with description Number line labeled from 80 to 112 with a bell-shaped curve above it. The curve reaches its highest point near 96 and decreases symmetrically toward both sides, approaching the number line near 80 and 112. The distribution is centered at 96.
11

Dwayne and Alisha both correctly graphed a standard normal curve. Which of the following statements is true?

A
Neither the means nor the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
B
The means of Dwayne’s and Alisha’s graphs must be the same but not the standard deviations.
C
The standard deviations of Dwayne’s and Alisha’s graphs must be the same but not the means.
D
Both the means and the standard deviations of Dwayne’s and Alisha’s graphs must be the same.
12

The mean test scores with standard deviations of four English classes are given. Class Mean Standard Deviation Mrs. Jones 89 1 point 9 Mrs. Rijo 82 1 point 4 Mr. Phan 73 3 point 4 Mrs. Scott 90 6 point 1 Which statement is most likely to be true?

A
The scores of Mrs. Jones’s class are the closest to the class mean.
B
The scores of Mrs. Scott’s class are the closest to the class mean.
C
The scores of Mrs. Rijo’s class are the closest to the class mean.
D
The scores of Mr. Phan’s class are the closest to the class mean.
13

A citizen wants to propose to the city council extending the hours at the local public library on some weekdays. To measure support for extended hours, the citizen visits neighborhood homes and asks adults the following: "Would you agree that the closing time of the library should be extended by one hour on weekdays to accommodate working families?” Of the 212 adults surveyed, 86 percent agreed with the statement. Which of the following statements about the results is true?

A
More families should be asked the same question to be sure of community support.
B
The survey suffers from voluntary response bias and may not estimate true support for the extended hours.
C
The 86 percent support provides substantial evidence that the library hours should be extended.
D
The survey suffers from question wording bias and may not represent true support for the extended hours.
15

Which of the following is a valid probability distribution?

A
Image with description The bar graph is titled Probability Distribution C. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 5 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 4, the 4th bar is at 5 and its height is 0 point 1, and the 5th bar is at 6 and its height is 0 point 1.
B
Image with description The bar graph is titled Probability Distribution B. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 4 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 3, the 4th bar is at 4 and its height is 0 point 3, the 5th bar is at 5 and its height is 0 point 2, and the 6th bar is at 6 and its height is 0 point 1.
C
Image with description The bar graph is titled as "Probability Distribution D". The horizontal axis ranges from 0 to 6 with increments of 1 and also labeled as X. The vertical axis ranges from 0 to 0 point 6 with increments of 0 point 1 and also labeled as a P subscript X of x. There are 5 bars on the coordinate plane. The first bar is located at 1 and its height is 0 point 2, the second bar is located at 2 and its height is 0 point 1, the third bar is located at 3 and its height is 0 point 1, the fourth bar is located at 4 and its height is 0 point 5, and the fifth bar is located at 6 and its height is 0 point 1.
D
Image with description The bar graph is titled Probability Distribution A. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 3 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph, and all the bars have a uniform height of 0 point 2.
17

The mean game scores and standard deviations of four seasons of a football team are given. Season Mean Standard Deviation 2005 19 3 point 5 2006 21 2 point 8 2007 12 1 point 0 2008 9 4 point 0 Which statement must be true?

A
The game scores of season 2007 have a greater spread than the game scores of season 2005.
B
The game scores of season 2006 have a greater spread than the game scores of season 2005.
C
The game scores of season 2006 have a greater spread than the game scores of season 2008.
D
The game scores of season 2005 have a greater spread than the game scores of season 2006.
18

An automotive service center would like feedback on its customer service. Each customer receives a printed card after they pay for services with a short survey on which customer service is ranked on a scale from 1 (least satisfied) to 5 (most satisfied). Customers can then choose to submit the card in a box on their way out of the store. The store manager finds that 140 cards were filled out in the past week, with an average customer satisfaction score of 2 point 4 7 Which type of bias is most likely to be present in the survey results?

A
This is question wording bias because the customer service score levels may not be clear to customers.
B
This is response bias because customers may not be truthful about their experience with customer service.
C
This is undercoverage bias because some types of customers may not have received cards.
D
This is nonresponse bias because many customers may choose to not fill out the cards.
20

The table shows the ages of houses to the nearest year in a neighborhood. Using the age of the houses as the random variable, cap x , which graph shows the probability distribution, cap p sub cap x times x , of a randomly chosen house?

A
Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and also labeled as x. The vertical axis ranges from 0 to 0 point 4 5 with increments of 0 point 0 5 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 1, the second bar is located at 2 and its height is 0 point 2, the third bar is located at 3 and its height is 0 point 3, and the fourth bar is located at 4 and its height is 0 point 4.
B
Image with description The bar graph is titled Probability Distribution. The horizontal axis lists 0 to 4 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 3 5 in increments of 0 point 0 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 1 and its height is 0 point 1 6, the second bar is at 2 and its height is 0 point 2 2, the 3rd bar is at 3 and its height is 0 point 2 8, and the 4th bar is at 4 and its height is 0 point 3 3.
C
Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and labeled as x. The vertical axis ranges from 0 to 0 point 3 5 with increments of 0 point 0 5 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 1 5, the second bar is located at 2 and its height is 0 point 2, the third bar is at 3 and its height is 0 point 2 5, and the fourth bar is located at 4 and its height is 0 point 3.
D
Image with description The bar graph is titled as "Probability Distribution". The horizontal axis ranges from 0 to 4 with increments of 1 and labeled as x. The vertical axis ranges from 0 to 0 point 1 4 with increments of 0 point 0 2 and labeled as a P subscript X of x. There are 4 bars on the graph. The first bar is located at 1 and its height is 0 point 6 5, the second bar is located at 2 and its height is 0 point 1, the third bar is located at 3 and its height is 0 point 1 2, and the fourth bar is located at 4 and its height is 0 point 1 3.

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