Question 1

A pharmaceutical company claims that their new drug reduces blood pressure by an average of 10 mmHg. A random sample of 40 patients who took the drug had a mean reduction of 8.5 mmHg with a standard deviation of 4 mmHg. At the 0.05 significance level, which is the correct null hypothesis for testing the company's claim?

Accepted Answer

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

Question 2

A researcher wants to test if the proportion of left-handed students at a university is different from the national average of 10%. In a sample of 200 students, 30 are left-handed. What is the correct test statistic to use for this hypothesis test?

Accepted Answer

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

Question 3

Which of the following statements about the $$p-$$value in hypothesis testing is correct?

Accepted Answer

The $$p-$$value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Question 4

A hospital administrator wants to compare the mean waiting times for two independent emergency rooms. Which test should be used to determine if there is a significant difference between the two means, assuming equal variances?

Accepted Answer

Two-sample $$t-$$test for independent samples with pooled variance

Question 5

A study compares the effectiveness of two diets by measuring weight loss in two independent groups. The 95% confidence interval for the difference in means is $$(-2.1, 0.5). $$What can be concluded?

Accepted Answer

There is not enough evidence to conclude a significant difference in mean weight loss between the two diets.

Question 6

Which formula is used to calculate the test statistic for comparing two population proportions?

Accepted Answer

$$z = \frac{(\hat{p}_1 - \hat{p}_2)}{\sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1$} + \frac{1}{n_2$})}}$$ where $$\hat{p} = \frac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 7

A psychologist measures stress levels in patients before and after therapy. Which statistical test is most appropriate for analyzing the difference in stress levels?

Accepted Answer

Paired $$t-$$test

Question 8

Which of the following is a property of the linear correlation coefficient $$r$$?

Accepted Answer

$$r is $$always between $$-1$$ and $$1.$$

Question 9

Given the regression equation $$\hat{y} = 2.5 + 0.8x$$, what is the predicted value of $$y$$ when $$x = 10$$?

Accepted Answer

$$10.5$$

Question 10

A researcher fits two models to a set of data. Model A has $$R^2 = 0.65$ and Model B has R^2$ = 0.72. $$Which model provides a better fit to the data?

Accepted Answer

Model B

Question 11

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

Accepted Answer

The samples are dependent.

Question 12

A company wants to test if the variance in delivery times from two warehouses is the same. Which test should be used?

Accepted Answer

F-test for equality of variances

Question 13

Which formula is used to calculate the test statistic for a hypothesis test about a single population variance?

Accepted Answer

$$\$$chi^2$$ = \frac{(n-1)s^2$}{\$$sigma_0$$^2}$$

Question 14

A genetics lab wants to test if the observed frequencies of four blood types in a sample match the expected frequencies based on known population proportions. Which test should be used?

Accepted Answer

Chi-square goodness-of-fit test

Question 15

Which of the following best describes the alternative hypothesis in a one-way ANOVA test?

Accepted Answer

At least one population mean is different from the others.

Question 16

A study finds a correlation coefficient of $$r = 0.95$$ between hours studied and exam scores. Which of the following is a correct interpretation?

Accepted Answer

There is a strong positive linear relationship between hours studied and exam scores.

Question 17

A researcher wants to test if the mean cholesterol level in a population is less than 200 mg/dL. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$H_1$$: \mu \u003c 200$$

Question 18

Which of the following is a correct interpretation of a 95% confidence interval for a population mean?

Accepted Answer

We are 95% confident that the interval contains the true population mean.

Question 19

A scientist wants to determine if a new fertilizer affects plant growth. She randomly assigns 30 plants to receive the new fertilizer and 30 plants to receive the standard fertilizer. Which statistical test should she use to compare the mean growth between the two groups?

Accepted Answer

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

Question 20

Which of the following is a property of the $$F-$$distribution used in ANOVA and variance tests?

Accepted Answer

It is always non-negative and right-skewed.

Chapters 8–12: Hypothesis Testing, Inferences from Two Samples, Correlation & Regression, Goodness-of-Fit, and ANOVA

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