Question 1

Which of the following best describes the Central Limit Theorem (CLT) for sample means?

Accepted Answer

The distribution of sample means approaches a normal distribution as the sample size increases, regardless of the population's distribution.

Question 2

A pharmaceutical company wants to compare the mean recovery times of two different drugs. Which statistical method is most appropriate?

Accepted Answer

Two-sample t-procedure for population means

Question 3

Suppose you are testing whether a new teaching method improves test scores. You measure the same students' scores before and after the method is applied. Which statistical technique should you use?

Accepted Answer

Paired t-test

Question 4

Which of the following is an assumption of the one-sample t-procedure for population means?

Accepted Answer

The data are a random sample from the population.

Question 5

A researcher wants to test if there is an association between smoking status (smoker/non-smoker) and incidence of lung disease (yes/no) in a population. Which test should be used?

Accepted Answer

Chi-square test for independence

Question 6

Which formula correctly represents the test statistic for a one-sample t-test?

Accepted Answer

$$ t = \frac{\bar{x} - \mu_0$}{s / \sqrt{n}} $$

Question 7

In a simple linear regression analysis, which of the following best describes the meaning of the slope coefficient?

Accepted Answer

It represents the expected change in the response variable for a one-unit increase in the explanatory variable.

Question 8

A hospital administrator wants to compare the mean waiting times for patients across four different departments. Which statistical method should be used?

Accepted Answer

One-way ANOVA

Question 9

Which of the following is a key assumption for the use of the two-sample t-test for independent samples?

Accepted Answer

The two samples are independent of each other.

Question 10

Which formula is used to calculate the degrees of freedom for a two-sample t-test with unequal variances (Welch's t-test)?

Accepted Answer

$$ df = \frac{\left( \frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$} \$$right)^2$$}{\frac{\left( \frac{s_1$^2}{n_1$} \$$right)^2$$}{n_1$ - 1} + \frac{\left( \frac{s_2$^2}{n_2$} \$$right)^2$$}{n_2$ - 1}} $$

Question 11

A study collects data on hours studied and exam scores for a group of students. The regression equation is $$ \hat{y} = 50 + 5x . $$What is the predicted exam score for a student who studied 4 hours?

Accepted Answer

$$ 70 $$

Question 12

Which of the following statements about the F-test in one-way ANOVA is correct?

Accepted Answer

It tests whether at least one group mean is different from the others.

Question 13

In multiple regression, which of the following is a potential problem if two explanatory variables are highly correlated?

Accepted Answer

Multicollinearity

Question 14

A researcher wants to test whether the distribution of blood types in a sample matches the known distribution in the general population. Which test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 15

Which of the following is the correct formula for the confidence interval for a population mean using the t-distribution?

Accepted Answer

$$ \bar{x} \pm t^* \frac{s}{\sqrt{n}} $$

Question 16

A two-way ANOVA is most appropriate when:

Accepted Answer

You want to study the effect of two categorical factors on a quantitative response variable.

Question 17

Which of the following is NOT an assumption of simple linear regression?

Accepted Answer

The explanatory variable must be categorical.

Question 18

A company wants to predict sales based on advertising spending and number of salespeople. Which statistical method should be used?

Accepted Answer

Multiple regression

Question 19

Which of the following best describes the purpose of using statistical inference?

Accepted Answer

To draw conclusions about a population based on sample data.

Question 20

A clinical trial compares the mean blood pressure reduction for two different medications. The sample sizes are small and population variances are unknown but assumed equal. Which test is most appropriate?

Accepted Answer

Pooled two-sample t-test

MATH 2209 – Introduction to Statistics II: Course Syllabus and Study Guide

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