Statistics Semester Review

Which of the following is the best estimate of the standard deviation of the distribution in the figure?

• 18

• 9

• 54

• 97

• 106

A company wanted to determine the child care costs of its employees. A sample of 25 employees were interviewed and their child care expenses for the previous year were determined. Later, the company discovered that the highest expense in the sample was mistakenly recorded as 5 times the actual amount. However, after correcting the error, the correct amount was still greater than or equal to any other expense in the sample. Which of the following sample statistics must have remained the same after the correction was made?

• variance

• mean

• mode

• range

• median

A company determines the mean and standard deviation of the employees' salaries in one year. What is the best description of the standard deviation?

• Approximately the median distance between the individual salaries of employees and the mean of every employee's salary.

• The amount of money separating the highest salary from the lowest salary when considering the middle 50% of the distribution.

• The amount of money separating the highest salary from the lowest salary when considering all employees.

• The distance between the salary of an employee and the mean salary of all the employees.

• Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries.

The equation of the LSRL for the points on a scatterplot is ŷ = 5.3-0.23x. What is the residual for the point (5, 4)?

• -0.15

• 0.15

• 1

• 0.62

• 0.85

Assuming that Joe and Matthew make their decisions independently, what is the probability that on a random trip to the bookstore, Matthew and Joe will each purchase 1 book? (use the probability distribution included)

• 0.1250

• 0.0625

• 0.2500

• 0.5000

• 0.7500

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Bella is at the 87th percentile in height for adult women, then her height, in inches, is closest to

• 63

• 67

• 66

• 72

• 70

To check the effect of hot temperatures on the elasticity of two brands of rubber bands, one box of Brand A and one box of Brand B rubber bands are tested. Ten bands from the Brand A box are placed in a warm car in the sun for two hours and ten bands from the Brand B box are kept at room temperature. The amount of stretch before the breakage is measured on each rubber band, and the mean for the hot bands is compared to the mean for the others. Is this a good experimental design?

• No, because the means are not proper statistics for comparison.

• No, because more than two brands should be used.

• No, because more temperatures should be used.

• No, because temperature is confounded with brand.

• Yes

Andrea's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.75. Which of the following is the best interpretation of this standardized score?

• Andrea's systolic blood pressure is 175.

• Andrea's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure of women her age.

• Andrea's systolic blood pressure is 1.75 above the average systolic blood pressure of women her age

• Only 1.75% of women Andrea's age have a higher systolic blood pressure than she does.

• Andrea's systolic blood pressure is 1.75 times the average systolic blood pressure of women her age.

The graph shows the distribution of scores of 30 students on a mathematics test. Based on the histogram, which statement must be true?

• The lowest test score is 41%.

• The highest test score is 100%.

• The mean test score is between 81% and 90%.

• The median test score is not greater than 80%.

• The lower quartile of the test scores is greater than 60%.

At a college the scores on the Spanish final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the Humanities final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the Spanish final and 84 on the Humanities final. Relative to the students in each respective class, in which subject did this student do better?

• The student did better in Spanish.

• The student did better in Humanities.

• There is no basis for comparison, since the subjects are different from each other and are in different departments.

• The student did equally well in each course.

• There is not enough information for comparison.