Question 1

A college wants to survey students about cafeteria satisfaction. The college randomly selects 50 students from the entire student roster using a random-number generator. What type of sampling is this, and why?

Accepted Answer

Simple random sampling, because every student has an equal chance of being selected.

Question 2

A city wants to study residents’ opinions on public transportation. The researcher randomly chooses five neighborhoods and surveys every household in those neighborhoods. What type of sampling is this?

Accepted Answer

Cluster sampling

Question 3

A professor surveys only the students who happen to visit office hours. What type of sampling is this?

Accepted Answer

Convenience sampling

Question 4

A school district groups teachers by grade level taught (elementary, middle, high school), and randomly selects 15 from each level. What type of sampling is this?

Accepted Answer

Stratified sampling

Question 5

A company lists employees numerically, randomly starts at 12, and surveys every 25th employee. What type of sampling is this?

Accepted Answer

Systematic sampling

Question 6

A researcher surveys 120 students from a university with 18,000 students to study phone usage. What is the population and what is the sample?

Accepted Answer

Population: 18,000 students; Sample: 120 students

Question 7

A city planning department finds that the average yearly household income from 520 households is $68,400. Is this value a statistic or a parameter?

Accepted Answer

Statistic, because it describes a sample.

Question 8

A basketball coach reviews data from 15 players and notes their average rebounds per game is 6.4. Is this value a statistic or a parameter?

Accepted Answer

Statistic, because it is based on a sample.

Question 9

A company emails a customer-satisfaction questionnaire and receives 310 responses. The average satisfaction rating among respondents is 4.6 out of 5. Is this value a statistic or a parameter?

Accepted Answer

Statistic, because it is based on a sample of respondents.

Question 10

Given the following counts for favorite music genres among 40 students: Pop (12), Hip-Hop (9), Country (7), Rock (8), Classical (4). Which genre accounts for more than 25% of all responses?

Accepted Answer

Pop

Question 11

Why is a side-by-side bar graph more appropriate than a pie chart for comparing preferred study environments by class standing?

Accepted Answer

Because a pie chart can only show one group at a time.

Question 12

A retail company randomly assigns 1,000 website visitors to see either a social-media ad or an email ad. What is the response variable in this experiment?

Accepted Answer

The click-through rate (CTR)

Question 13

In the experiment above, what are the levels of the treatment?

Accepted Answer

Social-media ad and email ad

Question 14

Refer to the first histogram (Daily Step Counts for 50 Clients). What is the shape of the distribution?

Accepted Answer

Bimodal

Question 15

Based on the first histogram, which interval contains the median number of steps?

Accepted Answer

7,000–8,000

Question 16

Refer to the second histogram (Daily Time Spent on a Mobile App). Describe the shape of the distribution.

Accepted Answer

Skewed right

Question 17

Based on the second histogram, which measure of central tendency is likely to be the largest?

Accepted Answer

Mean

Question 18

A nutritionist records the amount of sugar (in grams) in five granola bars: 9, 7, 11, 10, 13. What is the sample standard deviation $$s$$? (Round to two decimal places.)

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

Accepted Answer

$$2.24$$

Question 19

A hospital records wait times for patients. The distribution is bell-shaped with mean $$\mu = 18$$ minutes and standard deviation $$\sigma = 5$$ minutes. According to the Empirical Rule, between what two wait times do about 68% of patients fall?

$$ \mu \pm \sigma $$

Accepted Answer

$$13$$ and $$23$$ minutes

Question 20

Refer to the third image (two histograms of daily screen time). Both groups have the same mean. Which group has greater variability, and how can you tell?

Accepted Answer

The left group, because its data are more spread out.

Step-by-Step Guidance for Statistics Exam Practice

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