Question 1

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

Accepted Answer

A population includes all individuals of interest, while a sample is a subset selected from the population.

Question 2

A pharmaceutical company wants to test a new drug. They randomly assign 100 patients to receive the drug and 100 to receive a placebo. What type of study is this?

Accepted Answer

Controlled experiment

Question 3

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

Accepted Answer

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

Question 4

A histogram is best used to display which type of data?

Accepted Answer

Numerical (quantitative) data

Question 5

If a data set is highly skewed to the right, which measure of center is most appropriate to describe the typical value?

Accepted Answer

Median

Question 6

Which of the following is the formula for the standard deviation $$s of a $$sample of $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\bar{x}$$?

Accepted Answer

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

Question 7

A researcher finds a correlation coefficient $$r = -0.85$$ between hours spent watching TV and exam scores. What does this indicate?

Accepted Answer

There is a strong negative linear relationship.

Question 8

Which of the following is the equation for a least squares regression line predicting $$y$$ from $$x$$?

Accepted Answer

$$y = b_0$ + b_1$ x$$

Question 9

If the probability of event $$A is$$ $$0.3$$ and the probability of event $$B is$$ $$0.5$$, and $$A$$ and $$B$$ are independent, what is $$P(A \cap B)$$?

Accepted Answer

$$0.15$$

Question 10

A fair six-sided die is rolled. What is the probability of rolling a number greater than 4?

Accepted Answer

$$\frac{2}{6}$$

Question 11

Which of the following is the formula for a $$z-$$score for a value $$x$$ from a population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 12

A 95% confidence interval for a population mean is calculated as $$(50, 60). $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the population mean is between 50 and 60.

Question 13

Which of the following statements about the Central Limit Theorem is correct?

Accepted Answer

The sampling distribution of the sample mean will be approximately Normal if the sample size is large enough, regardless of the population distribution.

Question 14

A hypothesis test for a population proportion yields a p-value of 0.03. If the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 15

Which of the following is the formula for the margin of error $$E$$ for a confidence interval for a population proportion $$p at $$confidence level $$z^*$$ and sample size $$n$$?

Accepted Answer

$$E = z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 16

Which of the following is NOT a requirement for using the one-proportion $$z-$$test?

Accepted Answer

The population standard deviation is known.

Question 17

A boxplot is constructed for two different data sets. Data set A has a much longer right whisker than left, while Data set B has whiskers of equal length. What can you conclude?

Accepted Answer

Data set A is skewed right, Data set B is symmetric.

Question 18

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

Accepted Answer

Rejecting a true null hypothesis.

Question 19

A researcher wants to estimate the average height of all adult males in a city. She randomly selects 100 adult males and calculates a sample mean of 70 inches with a standard deviation of 3 inches. What is the standard error of the mean?

Accepted Answer

$$0.3$$

Introductory Statistics STA 2023 – Course Structure, Topics, and Study Guide

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