Question 1

Suppose a researcher collects a random sample of 50 patients' blood pressure readings. The population standard deviation is unknown. Which statistical concept justifies using the sample mean to estimate the population mean, and what distribution should be used for constructing a confidence interval?

Accepted Answer

The Central Limit Theorem; use the $$t-$$distribution

Question 2

A pharmaceutical company wants to compare the mean recovery times for two different drugs using independent samples. Which statistical test is most appropriate?

Accepted Answer

Two-sample $$t-$$test for difference in means

Question 3

A psychologist measures anxiety levels before and after therapy in the same group of patients. Which statistical method should be used to analyze the difference?

Accepted Answer

Matched pairs $$t-$$test

Question 4

Which of the following is a key assumption for the validity of the chi-squared goodness-of-fit test?

Accepted Answer

Expected cell counts should be at least 5

Question 5

A researcher wants to test whether the distribution of eye colors in a sample of 200 students matches the known distribution in the general population. Which test should be used?

Accepted Answer

Chi-squared goodness-of-fit test

Question 6

In a clinical trial, the following hypotheses are tested: $$H_0$$: \$$mu_1$$ = \$$mu_2 vs$$. $$H_A: \mu_1$ 
eq \mu_2$. If the p$-value is 0.03 and $$\, \alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is evidence of a difference in means

Question 7

Which formula correctly represents the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

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

Question 8

A study investigates whether smoking status (smoker/non-smoker) is independent of lung disease status (disease/no disease) in a sample of 500 adults. Which statistical test should be used?

Accepted Answer

Chi-squared test for independence

Question 9

A company wants to compare the mean productivity of employees across four different departments. Which statistical method is most appropriate?

Accepted Answer

One-way ANOVA

Question 10

Which of the following best describes the purpose of multiple regression analysis?

Accepted Answer

To model the relationship between one response variable and two or more predictor variables

Question 11

A researcher fits a regression model $$Y = \$$beta_0$$ + \$$beta_1$$ X_1$ + \$$beta_2$$ X_2$ + \varepsilon. $$What does $$\$$beta_2$$ represent?

Accepted Answer

The expected change in $$Y$$ for a one-unit increase in $$X_2$$, holding $$X_1$$ constant

Question 12

Which scenario requires the use of a two-way ANOVA?

Accepted Answer

Testing the effect of two categorical factors (e.g., diet and exercise) on blood pressure

Question 13

A researcher wants to determine if the mean test scores differ between students taught with three different teaching methods, while also considering the effect of gender. Which statistical method should be used?

Accepted Answer

Two-way ANOVA

Question 14

Which of the following is NOT an assumption of the one-way ANOVA?

Accepted Answer

The response variable is categorical

Question 15

A hospital administrator wants to know if the average length of stay differs between three hospitals. The data are approximately normal with equal variances. Which test should be used?

Accepted Answer

One-way ANOVA

Question 16

Which formula gives the test statistic for a two-sample $$t-$$test assuming equal variances?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{s_p \sqrt{\frac{1}{n_1$} + \frac{1}{n_2$}}}$$

Question 17

Which of the following best describes the null hypothesis for a chi-squared test for independence?

Accepted Answer

The two categorical variables are independent

Question 18

A researcher wants to predict house prices using square footage, number of bedrooms, and age of the house. Which statistical method should be used?

Accepted Answer

Multiple regression

Question 19

Which of the following is a critical difference between the chi-squared test for homogeneity and the chi-squared test for independence?

Accepted Answer

Test for homogeneity compares distributions across populations; test for independence assesses association within one population

MATH2209 Statistics Course Schedule and Key Topics (Winter 2026)

Study Guide - Practice Questions

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