Q: Jim buys his school supplies in bulk. On one shopping trip he bought 5 red pens at $$1.29 each, 3 blue pens at 1.49 $$each, 6 green pens at $$1.79 each, and 9 black pens at 0.99 $$each. What was the average cost of a pen?

$$\frac{(5 \times 1.29) + (3 \times 1.49) + (6 \times 1.79) + (9 \times 0.99)}{5 + 3 + 6 + 9} = \frac{6.45 + 4.47 + 10.74 + 8.91}{23} = \frac{30.57}{23} \approx 1.33$$

Question 1

Which of the following is an example of a qualitative variable?

Accepted Answer

The medal received (gold, silver, bronze) by an Olympic gymnast

Question 2

A researcher wants to estimate the average monthly utility bill for 3-bedroom homes using solar energy. She selects every 5th house from a list of all homes in the city. What sampling technique is being used?

Accepted Answer

Systematic sampling

Question 3

Determine whether the following variable is discrete or continuous: The number of students in a classroom.

Accepted Answer

Discrete

Question 4

A television station claims that the amount of advertising per hour of broadcast time has an average of 13 minutes and a standard deviation equal to 2.2 minutes. You watch the station for 1 hour and observe 16 minutes of advertising. What is the $$z-$$score for this amount?

Accepted Answer

$$z = \frac{16 - 13}{2.2} = 1.36$$

Question 5

Which level of measurement is represented by a student's favorite sport?

Accepted Answer

Nominal

Question 6

A sample of 25 community service projects is obtained and the scores are recorded as follows: 97, 96, 95, 99, 97, 100, 99, 95, 98, 100, 95, 97, 96, 100, 95, 98, 97, 99, 96, 100, 95, 97, 99, 97, 98. Which type of graph would best display the frequency of these scores?

Accepted Answer

Frequency histogram

Question 7

A statistics student interviews everyone in his apartment building to determine what percent of people own a cell phone. What sampling technique is used?

Accepted Answer

Cluster sampling

Question 8

Which of the following best describes the Empirical Rule for a bell-shaped distribution?

Accepted Answer

About 68% of the data falls within one standard deviation of the mean, about 95% within two, and about 99.7% within three.

Question 9

Jim buys his school supplies in bulk. On one shopping trip he bought 5 red pens at $$1.29 each, 3 blue pens at 1.49 $$each, 6 green pens at $$1.79 each, and 9 black pens at 0.99 $$each. What was the average cost of a pen?

Accepted Answer

$$\frac{(5 	imes 1.29) + (3 	imes 1.49) + (6 	imes 1.79) + (9 	imes 0.99)}{5 + 3 + 6 + 9} = \frac{6.45 + 4.47 + 10.74 + 8.91}{23} = \frac{30.57}{23} \approx 1.33$$

Question 10

Which of the following is a characteristic of a double-blind experiment?

Accepted Answer

Neither the experimental unit nor the researcher knows which treatment the experimental unit is receiving.

Question 11

Thirty-five math majors, 34 music majors, and 65 history majors are randomly selected from 244 math majors, 453 music majors, and 550 history majors at the state university. What sampling technique is used?

Accepted Answer

Stratified sampling

Question 12

The cholesterol levels (in milligrams per deciliter) of 30 adults are listed. Which measure is most resistant to outliers?

Accepted Answer

Median

Question 13

Which of the following variables is measured at the ratio level?

Accepted Answer

Weight capacity of a backpack

Question 14

A bag contains 80 cards, each with the name of an employee. Three names are picked from the bag. What sampling technique is used?

Accepted Answer

Simple random sampling

Question 15

A preschool teacher asks children to name their favorite color. The results are: purple, purple, green, blue, red, red, red, purple, red, green, red, green, blue, blue, blue, green, red, blue, red, yellow. What type of variable is 'favorite color'?

Accepted Answer

Nominal

Question 16

Which of the following best describes a frequency histogram?

Accepted Answer

A bar graph that shows the frequency of data values in intervals

Question 17

If the distribution of monthly utility bills is bell-shaped with a mean of $$132$$ and a standard deviation of $$10$$, what percentage of homes will have a monthly utility bill of more than $$122$$?

Accepted Answer

About 84%

Question 18

Which of the following is NOT a step in constructing a boxplot?

Accepted Answer

Calculate the mean

Question 19

Which measure of central tendency is most appropriate for skewed data?

Accepted Answer

Median

Question 20

Which formula is used to calculate the sample variance $$s^2$$?

Accepted Answer

$$s^2$$ = \frac{\sum (x_i - \bar{x}$$)^2$$}{n-1}$$

Statistics Practice Problems: Variables, Sampling, Data Analysis, and Graphs

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