Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A sample is a subset of a population.

Question 2

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

Accepted Answer

Experimental study

Question 3

Which of the following is a quantitative variable?

Accepted Answer

Number of children in a family

Question 4

A histogram is most appropriate for displaying which type of data?

Accepted Answer

Quantitative data

Question 5

Suppose the heights of adult women are approximately normally distributed with mean $$\mu = 64$$ inches and standard deviation $$\sigma = 2.5$$ inches. According to the 68-95-99.7 rule, approximately what percentage of women are between 61.5 and 66.5 inches tall?

Accepted Answer

68%

Question 6

Which of the following is the correct formula for the sample mean $$\bar{x} of$$ $$n$$ observations $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$

Question 7

A boxplot is especially useful for identifying which of the following in a dataset?

Accepted Answer

Outliers

Question 8

If a dataset is right-skewed, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 9

Which of the following statements about the standard deviation is TRUE?

Accepted Answer

It is affected by outliers.

Question 10

A correlation coefficient $$r of$$ $$-0.85$$ between two variables indicates:

Accepted Answer

A strong negative linear relationship

Question 11

In a simple linear regression, the equation of the least-squares regression line is $$\hat{y} = a + bx. $$What does the slope $$b$$ represent?

Accepted Answer

The change in $$y$$ for a one-unit increase in $$x$$

Question 12

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial.

Question 13

Suppose $$X is a $$binomial random variable with $$n = 10$$ and $$p = 0.3. $$What is the expected value $$E(X)$$?

Accepted Answer

$$E(X) = 3$$

Question 14

A 95% confidence interval for a population mean $$\mu is $$calculated as $$\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}. If $$the sample size $$n$$ increases, what happens to the width of the confidence interval?

Accepted Answer

It decreases.

Question 15

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 16

A p-value is defined as:

Accepted Answer

The probability, assuming the null hypothesis is true, of obtaining a result as extreme or more extreme than the observed result.

Question 17

Which of the following sampling methods is most likely to produce a representative sample?

Accepted Answer

Simple random sampling

Question 18

In a two-way table, the conditional distribution of one variable given another is useful for:

Accepted Answer

Comparing the distribution of one variable within levels of another variable

Question 19

Which of the following is an example of Simpson’s Paradox?

Accepted Answer

A trend that appears in several different groups of data reverses when the groups are combined.

Question 20

If the probability of an event A is $$0.3$$ and the probability of event B is $$0.5$$, and A and B are mutually exclusive, what is $$P(A \cup B)$$?

Accepted Answer

$$0.8$$

Introductory Statistics: Foundations, Data, and Descriptive Analysis

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