Q: Using the Empirical Rule (68–95–99.7 Rule), if the population mean is $$29.8$$ and the population standard deviation is $$5.2$$, about 95% of commute times should lie between which two values?

$$29.8 - 2 \times 5.2 = 19.4$$ and $$29.8 + 2 \times 5.2 = 40.2$$

Q: If the five-number summary for commute times is: Min = 18, Q1 = 25, Median = 30.5, Q3 = 34, Max = 40, what is the lower fence for detecting outliers?

$$Q_1 - 1.5$$ \times IQR = 25 - 1.5 \times 9 = 11.5$$

Question 1

A nutritionist studies whether a new diet reduces cholesterol. She selects 80 participants and measures their cholesterol before and after the diet. After 12 weeks, the average drop is 15 points. Which of the following best describes the parameter in this study?

Accepted Answer

The average cholesterol drop for all individuals who could possibly use the diet.

Question 2

Which of the following variables is quantitative, discrete, and measured at the ratio level?

Accepted Answer

Number of pets owned

Question 3

A researcher collects survey responses from college students about daily screen time and GPA. Which variable is most appropriately considered the explanatory variable?

Accepted Answer

Daily screen time

Question 4

A company surveys only employees at headquarters about remote work. What type of bias is most likely present?

Accepted Answer

Sampling bias

Question 5

A survey asked 200 households their favorite weekend activity. If 60 chose Sports and 50 chose Movies, what is the relative frequency for Sports?

Accepted Answer

$$0.30$$

Question 6

Given the following frequency distribution of quiz scores for 40 students:

40–49: 4
50–59: 6
60–69: 10
70–79: 12
80–89: 8

What percent of students scored 70 or higher?

Accepted Answer

$$\frac{12+8}{40} = 0.5 or$$ $$50\%$$

Question 7

Which of the following distributions is most likely to be bell-shaped?

Accepted Answer

Heights of 10-year-old boys

Question 8

Given the commute times (in minutes): 18, 22, 25, 28, 30, 31, 33, 35, 36, 40. What is the population mean $$\mu$$?

Accepted Answer

$$\mu = \frac{18+22+25+28+30+31+33+35+36+40}{10} = 29.8$$

Question 9

For the sample 18, 22, 25, 28, 30, what is the sample variance $$s^2$$?

Accepted Answer

$$s^2 = 23.8$

Question 10

Given the commute times: 18, 22, 25, 28, 30, 31, 33, 35, 36, 40, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q_3$ - Q_1$ = 34 - 25 = 9$$

Question 11

Using the Empirical Rule (68–95–99.7 Rule), if the population mean is $$29.8$$ and the population standard deviation is $$5.2$$, about 95% of commute times should lie between which two values?

Accepted Answer

$$29.8 - 2 	imes 5.2 = 19.4$$ and $$29.8 + 2 	imes 5.2 = 40.2$$

Question 12

A researcher wants to determine if a new teaching method improves test scores. She randomly assigns students to two groups: one uses the new method, the other uses the traditional method. Which best describes this study?

Accepted Answer

Experiment

Question 13

Which of the following is an example of response bias?

Accepted Answer

Some employees give 'safe' answers they think management wants.

Question 14

If the median commute time is 30.5 minutes and the mean is 29.8 minutes, what can you infer about the shape of the distribution?

Accepted Answer

Slightly skewed left

Question 15

Which of the following is NOT a characteristic of data measured at the ordinal level?

Accepted Answer

Differences between values are meaningful and measurable.

Question 16

A class of 40 students has quiz scores grouped into intervals. If the class width is 10, what are the lower and upper class limits of the third class if the first class is 40–49?

Accepted Answer

Lower class limit = 60, Upper class limit = 69

Question 17

Suppose a survey about favorite weekend activities finds that 0.15 of households prefer Reading. What percent is this?

Accepted Answer

$$0.15 	imes 100 = 15\%$$

Question 18

Which of the following best describes the level of measurement for temperature in Fahrenheit?

Accepted Answer

Interval

Question 19

If the five-number summary for commute times is: Min = 18, Q1 = 25, Median = 30.5, Q3 = 34, Max = 40, what is the lower fence for detecting outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR = 25 - 1.5 	imes 9 = 11.5$$

STA2023 Practice Midterm 1: Step-by-Step Statistics Study Guide

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