Q: A pharmaceutical company wants to test if a new drug lowers blood pressure more than the current standard. Which is the most appropriate alternative hypothesis $$H_a$$?

$$H_a: \mu_{\text{new}} \u003c \mu_{\text{standard}}$$

Q: Which formula is used to calculate the expected count in a cell for a chi-square test for independence?

$$\text{Expected count} = \dfrac{\text{Row total} \times \text{Column total}}{\text{Grand total}}$$

Question 1

Which of the following best describes the null hypothesis $$H_0 in a $$hypothesis test for the mean of a population?

Accepted Answer

It claims that the population mean is equal to a specified value.

Question 2

A pharmaceutical company wants to test if a new drug lowers blood pressure more than the current standard. Which is the most appropriate alternative hypothesis $$H_a$$?

Accepted Answer

$$H_a: \mu_{	ext{new}} \u003c \mu_{	ext{standard}}$$

Question 3

Which formula is used to calculate the test statistic for a one-sample $$z-$$test for the mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n}}$$

Question 4

A researcher is comparing the mean cholesterol levels between two independent groups. Which test should be used?

Accepted Answer

Two-sample $$t-$$test for independent samples

Question 5

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

Accepted Answer

The probability of observing data as extreme as the sample, assuming the null hypothesis is true.

Question 6

A hospital wants to know if the proportion of patients recovering from a new treatment is different from the national average. Which test is most appropriate?

Accepted Answer

One-sample $$z-$$test for proportions

Question 7

Which formula is used to calculate the confidence interval for a population mean when the population standard deviation is unknown?

Accepted Answer

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

Question 8

In a study of smoking and lung cancer, which test would you use to determine if there is an association between smoking status (smoker/non-smoker) and lung cancer diagnosis (yes/no)?

Accepted Answer

Chi-square test for independence

Question 9

A scientist wants to compare the mean weight loss between three different diets. Which statistical test should be used?

Accepted Answer

ANOVA (Analysis of Variance)

Question 10

Which of the following is NOT an assumption for the two-sample $$t-$$test for independent samples?

Accepted Answer

The samples are paired.

Question 11

A researcher collects data on hours studied and exam scores for 100 students. Which statistic measures the strength and direction of the linear relationship between these two variables?

Accepted Answer

Correlation coefficient $$r$$

Question 12

Which formula is used to calculate the expected count in a cell for a chi-square test for independence?

Accepted Answer

$$	ext{Expected count} = \dfrac{	ext{Row total} 	imes 	ext{Column total}}{	ext{Grand total}}$$

Question 13

A medical researcher wants to test if the mean recovery time for a new therapy is less than 10 days. The sample mean is 8.5 days, sample standard deviation is 2 days, and sample size is 25. What is the value of the test statistic?

Accepted Answer

$$t = \dfrac{8.5 - 10}{2 / \sqrt{25}} = -3.75$$

Question 14

Which of the following best describes the purpose of a paired $$t-$$test?

Accepted Answer

To compare means from the same group measured at two different times.

Question 15

A study finds a $$p-$$value of 0.03 when testing $$H_0$$: \mu = 50$$ against H_a$$: \mu 
eq 50$$ at $$\alpha = 0.05$$. What is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is significant evidence that $$\mu 
eq 50.$$

Question 16

Which formula is used to calculate the test statistic for a two-sample $$t-$$test assuming equal variances?

Accepted Answer

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

Question 17

Which of the following is a correct definition of Type I error in hypothesis testing?

Accepted Answer

Rejecting a true null hypothesis.

Question 18

A researcher wants to test if the proportion of defective products in a factory is less than 5%. In a sample of 200 products, 6 are defective. What is the sample proportion?

Accepted Answer

$$\hat{p} = \dfrac{6}{200} = 0.03$$

Question 19

Which formula is used to calculate the test statistic for a one-sample $$z-$$test for proportions?

Accepted Answer

$$z = \dfrac{\hat{p} - p_0$}{\sqrt{\dfrac{p_0$ (1 - p_0$)}{n}}}$$

Final Exam Topics Overview: Statistics Concepts and Methods

Study Guide - Practice Questions

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