Question 1

Which of the following best describes the primary goal of descriptive statistics?

Accepted Answer

To summarize and visualize data in a meaningful way.

Question 2

A researcher collects data on the number of hours students study per week and their exam scores. Which statistical method is most appropriate to model the relationship between these two variables?

Accepted Answer

Linear regression

Question 3

Which formula represents the calculation of the sample mean $$\bar{x}$$ for a dataset with $$n$$ values $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

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

Question 4

A hospital administrator wants to estimate the average wait time in the emergency room. She randomly selects 50 patients and calculates a 95% confidence interval for the mean wait time. What does this confidence interval represent?

Accepted Answer

If many samples were taken, about 95% of the calculated intervals would contain the true mean wait time.

Question 5

Which of the following is a correct application of the Central Limit Theorem?

Accepted Answer

The distribution of sample means will be approximately normal if the sample size is large enough, regardless of the population's distribution.

Question 6

A pharmaceutical company tests a new drug and wants to know if it is more effective than the current standard. Which statistical method should they use to make a decision based on sample data?

Accepted Answer

Hypothesis testing

Question 7

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

Accepted Answer

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

Question 8

A student claims that the average time spent on homework per week by all students at FAU is 10 hours. You collect a random sample and perform a hypothesis test. What is the null hypothesis $$H_0$$?

Accepted Answer

$$H_0$$: \mu = 10$$

Question 9

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

Accepted Answer

Rejecting a true null hypothesis.

Question 10

Suppose the correlation coefficient $$r$$ between two variables is $$-0.85. $$What does this indicate about the relationship between the variables?

Accepted Answer

There is a strong negative linear relationship.

Question 11

A company wants to know if a new training program increases employee productivity. They collect productivity data before and after the program for a random sample of employees. Which statistical test is most appropriate?

Accepted Answer

Paired t-test

Question 12

Which formula gives the probability of event $$A in a $$sample space $$S$$?

Accepted Answer

$$P(A) = \frac{n(A)}{n(S)}$$

Question 13

A researcher wants to estimate the proportion of students who prefer online classes. Which formula should be used to calculate a 95% confidence interval for the population proportion $$p$$ based on a sample proportion $$\hat{p}$$ and sample size $$n$$?

Accepted Answer

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

Question 14

Which of the following is NOT a requirement for using the Central Limit Theorem?

Accepted Answer

The population must be normally distributed.

Question 15

A dataset contains the following values: 2, 4, 4, 6, 8. What is the median?

Accepted Answer

4

Question 16

Which formula represents the equation of a simple linear regression line predicting $$y$$ from $$x$$?

Accepted Answer

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

Question 17

A university wants to compare the average GPA of students in three different majors. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 18

Which of the following statements about $$p-$$values is correct?

Accepted Answer

A small $$p-$$value indicates strong evidence against the null hypothesis.

STA 2023 Introductory Statistics Syllabus & Study Guide

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