Question 1

Which of the following best describes the difference between descriptive and inferential statistics?

Accepted Answer

Descriptive statistics summarize and organize data, while inferential statistics use data from a sample to make conclusions about a population.

Question 2

A researcher wants to compare the average price per ounce of a brand of cereal at two different grocery stores. She randomly selects 30 varieties from each store. Which statistical method is most appropriate to test if there is a significant difference in mean prices between the two stores?

Accepted Answer

A two-sample t-test for means

Question 3

Which of the following is NOT a requirement for constructing a valid confidence interval for a population mean?

Accepted Answer

The population must be finite.

Question 4

Suppose you are testing the claim that the mean GPA of students at University A is higher than at University B. Which of the following is the correct null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: \mu_A \leq \mu_B$$

Question 5

A sample of 50 patients is selected from a hospital to estimate the average recovery time after a new treatment. The sample mean is 8 days, and the sample standard deviation is 2 days. Construct a 95% confidence interval for the population mean recovery time. Which formula should be used?

Accepted Answer

$$\bar{x} \pm t_{\alpha/2, n-1} \cdot \dfrac{s}{\sqrt{n}}$$

Question 6

Which of the following best describes the Central Limit Theorem?

Accepted Answer

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Question 7

A pharmaceutical company claims that its new drug cures 80% of patients. In a clinical trial of 100 patients, 72 are cured. What is the value of the sample proportion ($$\hat{p}$$)?

Accepted Answer

$$\hat{p} = 0.72$$

Question 8

Which of the following is an example of a discrete random variable?

Accepted Answer

The number of text messages sent by a student in a day

Question 9

A researcher wants to estimate the proportion of defective products in a factory. She takes a random sample of 200 products and finds 12 are defective. What is the point estimate for the population proportion?

Accepted Answer

$$\dfrac{12}{200}$$

Question 10

Which of the following statements about hypothesis testing is TRUE?

Accepted Answer

A Type I error occurs when a true null hypothesis is rejected.

Question 11

In a study comparing the mean number of goals scored by two soccer teams over a season, which of the following would be an appropriate alternative hypothesis ($$H_a) if $$you want to test whether Team A scores more goals on average than Team B?

Accepted Answer

$$H_a: \mu_A \u003e \mu_B$$

Question 12

A histogram of exam scores for a class is bell-shaped and symmetric. Which measure of central tendency is most appropriate to describe the center of this distribution?

Accepted Answer

Mean

Question 13

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

Accepted Answer

Simple random sampling

Question 14

If the 95% confidence interval for the mean price of a product is $$(4.50, 5.50)$$, which of the following statements is correct?

Accepted Answer

We are 95% confident that the true mean price is between $$4.50$$ and $$5.50.$$

Question 15

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

Accepted Answer

$$\dfrac{1}{3}$$

Question 16

Which of the following is a correct interpretation of a p-value in hypothesis testing?

Accepted Answer

The probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

Question 17

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the z-score for a value of $$x = 130$$?

Accepted Answer

$$z = \dfrac{130 - 100}{15} = 2$$

Question 18

Which of the following is a potential source of bias in a statistical study comparing the prices of products at two stores?

Accepted Answer

Selecting only products that are on sale at one store

Question 19

A student calculates the variance of a sample of exam scores to be $$16. $$What is the standard deviation?

Accepted Answer

$$4$$

Question 20

In a hypothesis test, the significance level is set at $$\alpha = 0.05. $$What does this mean?

Accepted Answer

There is a 5% risk of rejecting the null hypothesis when it is actually true.

Elementary Statistics: Course Syllabus and Study Guide Overview

Guida di studio - Domande di pratica

Study guide - Flashcard