Q: If the population mean commute time is $$\mu = 29.8$$ and the standard deviation is $$\sigma = 7.2$$, about 95% of commute times should fall between which two values?

$$29.8 \pm 2 \times 7.2 = [15.4, 44.2]$$

Q: In a population of 83 residents, 36 are male and 47 are female. What is the probability that a randomly selected resident is female?

$$P(\text{female}) = \frac{47}{83}$$

Q: Given the education levels of residents: High school only (27), Some college (24), Bachelor's degree (19), Graduate degree (13). What is the probability that a resident has at least a bachelor's degree?

$$P(\text{at least bachelor's}) = \frac{19 + 13}{83} = \frac{32}{83}$$

Question 1

A nutritionist selects 80 participants and measures their cholesterol before and after a diet. After 12 weeks, the average drop is 15 points. In this scenario, what is the parameter?

Accepted Answer

The average cholesterol drop of all people who could possibly use the diet

Question 2

Which of the following is a quantitative, continuous variable?

Accepted Answer

Temperature in Fahrenheit on a given day

Question 3

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

Accepted Answer

Sampling bias

Question 4

Given the following frequency distribution of quiz scores for 40 students:
Interval: 40-49 (6), 50-59 (4), 60-69 (12), 70-79 (8), 80-89 (8), 90-99 (2)
What are the lower and upper class limits of the 3rd class?

Accepted Answer

Lower: 60, Upper: 69

Question 5

A survey asked 200 households their favorite weekend activity. 60 chose sports, 50 chose movies, 40 chose shopping, and 30 chose reading. What is the relative frequency of households that prefer sports?

Accepted Answer

$$\frac{60}{200} = 0.30$$

Question 6

Which of the following best describes a distribution that is bell-shaped?

Accepted Answer

Heights of 10-year-old boys

Question 7

Given the daily commute times (in minutes) for 10 employees: 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 8

Suppose you select the first 5 commute times as a sample: 18, 22, 25, 28, 30. What is the sample mean $$\bar{x}$$?

Accepted Answer

$$\bar{x} = \frac{18 + 22 + 25 + 28 + 30}{5} = 24.6$$

Question 9

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

Accepted Answer

$$s^2$$ = \frac{$$(18-24.6)^2$$ + $$(22-24.6)^2$$ + $$(25-24.6)^2$$ + $$(28-24.6)^2$$ + $$(30-24.6)^2$$}{4} = 22.3$$

Question 10

Given the five-number summary: minimum = 18, Q1 = 22, median = 25, Q3 = 28, maximum = 30, what is the interquartile range (IQR)?

Accepted Answer

$$IQR = Q3 - Q1 = 28 - 22 = 6$$

Question 11

If the population mean commute time is $$\mu = 29.8$$ and the standard deviation is $$\sigma = 7.2$$, about 95% of commute times should fall between which two values?

Accepted Answer

$$29.8 \pm 2 	imes 7.2 = [15.4, 44.2]$$

Question 12

In a population of 83 residents, 36 are male and 47 are female. What is the probability that a randomly selected resident is female?

Accepted Answer

$$P(	ext{female}) = \frac{47}{83}$$

Question 13

Given the education levels of residents: High school only (27), Some college (24), Bachelor's degree (19), Graduate degree (13). What is the probability that a resident has at least a bachelor's degree?

Accepted Answer

$$P(	ext{at least bachelor's}) = \frac{19 + 13}{83} = \frac{32}{83}$$

Question 14

If two residents are selected at random (with replacement), what is the probability that both have only a high school education?

Accepted Answer

$$P = \left(\frac{27}{83}\$$right)^2$$

Question 15

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

Accepted Answer

GPA

Question 16

Which of the following scenarios best illustrates nonresponse bias?

Accepted Answer

Only 20% of employees respond, mostly those unhappy with remote work

Question 17

Which of the following is a qualitative, nominal variable?

Accepted Answer

Type of car transmission (manual, automatic, CVT)

Question 18

A distribution of waiting times at a restaurant, where most are short but a few are very long, is most likely:

Accepted Answer

Skewed right

STA2023 Review: Data Collection, Summarizing Data, and Probability

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