Q: A survey of 930 adults asked how much they spend in preparation for personal travel each year. The frequency distribution is as follows: 0–99: 380, 100–199: 230, 200–299: 210, 300–399: 50, 400–499: 60. What is the estimated sample mean using class midpoints?

Estimated mean $$= \frac{(49.5 \times 380) + (149.5 \times 230) + (249.5 \times 210) + (349.5 \times 50) + (449.5 \times 60)}{930}$$

Q: You are calculating your English grade with the following scores and weights: Tests: 82 (70%), Quizzes: 91 (20%), Participation: 95 (10%). What is your weighted average?

Weighted average $$= (82 \times 0.7) + (91 \times 0.2) + (95 \times 0.1) = 84.1$$

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a value calculated from a population, while a statistic is calculated from a sample.

Question 2

A survey of 930 adults asked how much they spend in preparation for personal travel each year. The frequency distribution is as follows: 0–99: 380, 100–199: 230, 200–299: 210, 300–399: 50, 400–499: 60. What is the estimated sample mean using class midpoints?

Accepted Answer

Estimated mean $$= \frac{(49.5 	imes 380) + (149.5 	imes 230) + (249.5 	imes 210) + (349.5 	imes 50) + (449.5 	imes 60)}{930}$$

Question 3

Which sampling method is most appropriate for selecting a group of students from a university where the population is divided by major, and you want to ensure each major is represented?

Accepted Answer

Stratified sample

Question 4

Given the following data set of ages: 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 65. Which measure of central tendency best describes a typical entry, and why?

Accepted Answer

Median, because it is resistant to the outlier (65).

Question 5

A nurse worked 54 hours last week. If the mean number of hours worked by 24 nurses is 40 hours with a standard deviation of 8 hours, what is the z-score for this nurse?

Accepted Answer

z-score $$= \frac{54 - 40}{8} = 1.75$$

Question 6

In a study, the sample mean height of women (ages 20–29) is 64.2 inches with a sample standard deviation of 2.9 inches. Using the Empirical Rule, what percent of women are expected to have heights between 58.4 inches and 64.2 inches?

Accepted Answer

About 34%

Question 7

You are calculating your English grade with the following scores and weights: Tests: 82 (70%), Quizzes: 91 (20%), Participation: 95 (10%). What is your weighted average?

Accepted Answer

Weighted average $$= (82 	imes 0.7) + (91 	imes 0.2) + (95 	imes 0.1) = 84.1$$

Question 8

Lockheed Martin hired 5 college graduates with starting salaries (in $1000s): 41, 38, 39, 45, 47. What is the population variance?

Accepted Answer

Population variance $$= \frac{\sum (x - \mu)^2$}{N}$$

Question 9

A frequency distribution has a minimum value of 155 and a maximum value of 405. If you want 7 classes, what is the class width?

Accepted Answer

Class width $$= \frac{405 - 155}{7} \approx 35.7$$, round up to 36

Question 10

Which chart is most appropriate for displaying the number of motor vehicle thefts in the U.S. from 2005 to 2015?

Accepted Answer

Time series chart

Question 11

The five-number summary consists of which values?

Accepted Answer

Minimum, Q1, Median, Q3, Maximum

Question 12

If the mean speed of vehicles is 56 mph with a standard deviation of 4 mph, what is the z-score for a car traveling at 47 mph?

Accepted Answer

z-score $$= \frac{47 - 56}{4} = -2.25$$

Question 13

Using Chebyshev’s Theorem, what proportion of households have between 0 and 4 pets if the mean is 2 and the standard deviation is 1?

Accepted Answer

At least $$1 - \frac{1}{2^2$} = 0.75 or 75$$% of households

Question 14

Which of the following is a qualitative variable?

Accepted Answer

Type of degree earned

Question 15

A scatterplot is most useful for:

Accepted Answer

Displaying the relationship between two quantitative variables

Question 16

The coefficient of variation is calculated as:

Accepted Answer

Coefficient of variation $$= \frac{	ext{standard deviation}}{	ext{mean}} 	imes 100\%$$

Question 17

Which chart is best for showing the relative sizes of categories, such as the number of degrees conferred by type?

Accepted Answer

Pie chart

Question 18

If a frequency distribution table has class midpoints and frequencies, which formula estimates the mean?

Accepted Answer

Estimated mean $$= \frac{\sum (x 	imes f)}{\sum f}$$

Question 19

Which of the following is NOT a type of sampling method?

Accepted Answer

Pie sampling

Step-by-Step Guidance for Chapter 2 Introductory Statistics Word Problems

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