Chapter 5 AP Stats Review

This is a standard deviation contest. Which of the following sets of four numbers has the largest possible standard deviation?

• 7, 8, 9, 10

• 1, 2, 9, 10

• 0, 0, 10, 10

• 0, 1, 2, 3

• 5, 5, 5, 5

Birth weights at a local hospital have a normal distribution with a mean of 110 ounces and a standard deviation of 15 ounces. The proportion of infants with birthweights between 125 ounces and 140 ounces is:

• 0.819

• 0.636

• 0.477

• 0.158

• 0.136

The distribution of actual weights of 8.0-ounce chocolate bars produced by a certain machine is normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. The proportion of chocolate bars weighing less than or equal to 8.0 ounces is:

• 0.159

• 0.341

• 0.500

• 0.659

• 0.841

A study found a correlation of r = 0.61 between the age of an employee and his or her income. You may correctly conclude that:

• An increase in an employee’s age causes an increase in their income.

• As an employee’s age increases, their income tends to increase.

• There is no association between an employee's age and his or her income.

• As an employee’s age increases, their income tends to decrease.

• There is a 61% change we can accurately predict an employee’s income if we know their age.

A student wonders if people of similar heights tend to date each other. She measures herself, her dormitory roommate, and the women in the adjoining rooms; then she measures the next man each woman dates. Here are the data (heights in inches): Women: 66, 64, 66, 65, 70, 65 Men: 72, 68, 70, 68, 74, 69 What can be concluded from the data?

• The variables measured are all categorical.

• There is a strong negative association between the heights of men and women, since the women are always smaller than the men they date.

• Tall women tend to date short men.

• Any height above 70 inches must be considered an outlier.

• There is a positive association between the heights of men and women who date each other.

The following computer output describes the relationship between y = height (in cm) and x = foot length (also in cm) for 12 randomly selected students from the British Census @ Schools database. The scatterplot for this relationship show a roughly linear shape. Which of the following is an equation of least-squares regression line for these data?

• Height = 117.99 + 1.878 (Foot Length)

• Foot Length = 117.99 + 1.878 (Height)

• Height = 1.878 + 117.99 (Foot Length)

• Foot Length = 1.878 + 117.99 (Height)

One concern about the depletion of the ozone layer is that the increase in ultraviolet (UV) light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV, measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed with the following results: The least-squares regression line is the line that

• minimizes the sum of the distances between the actual UV values and the predicted UV values.

• minimizes the sum of the squared residuals between the actual yield and the predicted yield.

• minimizes the sum of the distances between the actual yield and the predicted UV.

• minimizes the sum of the squared residuals between the actual UV reading and the predicted UV values.

• minimizes the perpendicular distance between the regression line and each data point.

Which value is in the top 25% of the data?

• 16

• 22

• 29

• 36

Independently selected groups of middle-school children were given a poem to memorize. After a certain period of time, they were asked to recall as much of the poem as they could. A back-to-back stem plot of the distribution of the number of words that each group of children could correctly remember is displayed above. Which of the following statements about these data is true?

• There are more students in Group 1 than in Group 2.

• The third quartile of the Group 1 distribution is larger than the maximum value of the Group 2 distribution (that is, 25% of the Group 1 values are larger than any Group 2 value).

• The median of the Group 2 distribution is smaller than the first quartile of the Group 1 distribution (that is, 50% of the Group 2 values are smaller than at least 75% of Group 1 values).

• The mean number of words remembered for Group 1 is smaller than the mean number of words remember for Group 2.

The side-by-side boxplots show the distribution of test scores in Ms. Williams’s two sections of calculus. Based on these boxplots, which one of the following statements must be true?

• The lowest score in A period was close to the 15th percentile of the C period class.

• The mean score for students in C period was higher than the mean score for students in A period.

• More people scored between 72 and 90 in C period than scored between 72 and 81 in A period.

• The standard deviation of scores in A period is smaller than the standard deviation of scores in C period.