Question 1

A researcher wants to estimate the average number of hours college students spend studying per week. She surveys 200 students from her university. Is the value she calculates from her sample a parameter or a statistic?

Accepted Answer

It is a statistic because it is calculated from a sample of students.

Question 2

Which of the following variables is quantitative and discrete?

Accepted Answer

The number of books a student owns.

Question 3

A hospital wants to know if adults who are 20 to 30 years old get more sleep in Europe or in the United States. What is the population in this study?

Accepted Answer

Adults who are 20 to 30 years old in Europe and the United States.

Question 4

A company wants to survey its customers about their satisfaction. Using their customer database, the company randomly selects 100 customers from each of five different regions. What type of sampling is used?

Accepted Answer

Stratified sampling

Question 5

A medical researcher wants to study the effect of a new drug on blood pressure. She randomly assigns 100 patients to receive the drug and 100 patients to receive a placebo. What type of study is this?

Accepted Answer

A designed experiment

Question 6

Which of the following is an example of response bias in a survey?

Accepted Answer

Respondents giving answers they think are socially acceptable rather than truthful.

Question 7

Given the following frequency distribution for the number of customers waiting for a table at a restaurant at 6:00 PM:

Number: 1-3, 4-6, 7-9, 10-12
Frequency: 5, 8, 4, 3

What is the relative frequency for the 4-6 customers category? (Round to two decimal places as needed.)

Accepted Answer

$ \frac{8}{20} = 0.40 $

Question 8

A histogram of a data set shows a long tail to the right. Which measure of central tendency is likely to be greater than the others?

Accepted Answer

The mean

Question 9

A sample of 10 students has the following test scores: 70, 75, 80, 85, 90, 95, 100, 105, 110, 115. What is the interquartile range (IQR) of this data set?

Accepted Answer

$ 30 $

Question 10

A researcher collects the following data on the weights (in grams) of 8 candies: 0.81, 0.83, 0.84, 0.85, 0.86, 0.88, 0.89, 0.90. What is the mean weight?

Accepted Answer

$ \frac{0.81 + 0.83 + 0.84 + 0.85 + 0.86 + 0.88 + 0.89 + 0.90}{8} = 0.8575 $

Question 11

Which of the following best describes the standard deviation?

Accepted Answer

The square root of the variance.

Question 12

A company wants to compare the heights of male and female employees. The mean height of males is 175 cm with a standard deviation of 8 cm. The mean height of females is 165 cm with a standard deviation of 6 cm. Which group has more relative variation in height?

Accepted Answer

Males, because $ \frac{8}{175} = 0.0457 $ is greater than $ \frac{6}{165} = 0.0364 $.

Question 13

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 60?

Accepted Answer

$ z = \frac{60 - 50}{5} = 2 $

Question 14

A researcher wants to know if there is a relationship between exercise frequency (measured in days per week) and cholesterol level (measured in mg/dL). Which type of graph is most appropriate to display the relationship?

Accepted Answer

A scatterplot

Question 15

Which of the following statements about the Empirical Rule is correct?

Accepted Answer

Approximately 68% of the data falls within one standard deviation of the mean in a bell-shaped distribution.

Question 16

A pie chart is best used for which type of data?

Accepted Answer

Categorical data

Question 17

A frequency distribution of exam scores is right-skewed. Which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 18

A researcher wants to compare the effectiveness of two diets. She randomly assigns 50 participants to each diet and measures their weight loss after 3 months. Which of the following best describes the explanatory and response variables?

Accepted Answer

Explanatory variable: type of diet; Response variable: weight loss

Question 19

A study finds that the median household income in a city is $45,000, while the mean is $60,000. What does this suggest about the distribution of incomes?

Accepted Answer

The distribution is right-skewed.

Fundamental Concepts and Applications in Introductory Statistics

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