Question 1

Which of the following best describes the difference between an observational study and an experimental study?

Accepted Answer

An observational study collects data without influencing the subjects, while an experimental study involves the researcher actively assigning treatments to subjects.

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

Experimental study

Question 3

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

Accepted Answer

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

Question 4

A data set of exam scores is strongly skewed to the right. Which measure of center is most appropriate to describe the typical score?

Accepted Answer

Median

Question 5

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

Accepted Answer

$$s is $$always greater than or equal to zero.

Question 6

If the probability of a patient recovering from a disease after treatment is 0.8, what is the probability that two randomly selected patients both recover?

Accepted Answer

$$0.8 	imes 0.8 = 0.64$$

Question 7

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

Accepted Answer

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

Question 8

Which of the following is the correct formula for the z-score of a value $$x in a $$data set with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

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

Question 9

According to the Central Limit Theorem, as the sample size $$n$$ increases, the distribution of the sample mean $$\bar{x}$$:

Accepted Answer

Approaches a normal distribution regardless of the population distribution

Question 10

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

Accepted Answer

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

Question 11

Which of the following is the correct formula for the margin of error $$E in a $$confidence interval for a population mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$E = z^* \frac{\sigma}{\sqrt{n}}$$

Question 12

A researcher wants to estimate the proportion of students who prefer online classes. She surveys 200 students and finds that 120 prefer online classes. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{120}{200} = 0.6$$

Question 13

Which of the following is NOT an assumption for using the normal distribution to construct a confidence interval for a population mean?

Accepted Answer

The data are categorical.

Question 14

A hypothesis test is conducted at the 5% significance level ($$\alpha = 0.05). $$The p-value is 0.03. What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

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 hospital administrator wants to know if a new training program reduces the average time to respond to emergencies. Which is the correct null hypothesis $$H_0$$ for this scenario?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$

Question 17

Which of the following is the correct formula for the standard error of the sample mean $$SE_{\bar{x}}$$ when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$SE_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$

Question 18

A study finds a correlation coefficient $$r = 0.85$$ between hours studied and exam score. Which of the following is the best interpretation?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam score.

Question 19

Which of the following is a discrete random variable?

Accepted Answer

The number of patients arriving at an emergency room in an hour.

Elementary Statistics I – Course Syllabus and Study Guide

Guida di studio - Domande di pratica

Study guide - Flashcard