Question 1

A pharmaceutical company wants to compare the mean blood pressure reduction between two independent groups: one receiving Drug A and one receiving Drug B. Which statistical test should be used if the population variances are assumed equal and both samples are random and independent?

Accepted Answer

Pooled two-sample t-test

Question 2

A researcher wants to estimate the mean weight of newborns in a city. The population standard deviation $$\sigma is $$known to be 450 grams. Which formula should be used to construct a 95% confidence interval for the mean?

Accepted Answer

$$\bar{x} \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$$

Question 3

Which of the following best describes the power of a statistical test?

Accepted Answer

The probability of correctly rejecting the null hypothesis when it is false

Question 4

In a study comparing the mean cholesterol levels before and after a dietary intervention in the same group of patients, which test is most appropriate?

Accepted Answer

Paired t-test

Question 5

A scientist wants to test if the variance of a new manufacturing process is less than the old process. Which test should be used to compare the variances of two independent samples?

Accepted Answer

F-test for equality of variances

Question 6

If the sample size $$n is $$large and the population standard deviation $$\sigma is $$unknown, which formula should be used for the confidence interval for the mean?

Accepted Answer

$$\bar{x} \pm z_{\alpha/2} \frac{s}{\sqrt{n}}$$

Question 7

A hospital wants to determine if the mean recovery time for patients using a new therapy is different from the standard recovery time of 14 days. The null hypothesis is $$H_0$$: \mu = 14$$. Which of the following represents a two-sided alternative hypothesis?

Accepted Answer

$$H_a: \mu 
eq 14$$

Question 8

Which of the following is a requirement for using the pooled two-sample t-test?

Accepted Answer

The population variances must be equal

Question 9

A researcher is comparing two independent samples where the population variances are not equal. Which formula should be used for the test statistic?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

Question 10

In hypothesis testing, what does a Type I error represent?

Accepted Answer

Rejecting the null hypothesis when it is true

Question 11

A study uses the Wilcoxon's Signed Rank Test to compare pre- and post-treatment scores for patients. Which of the following is a requirement for this test?

Accepted Answer

The differences must be symmetrically distributed

Question 12

A researcher wants to determine the minimum sample size needed to estimate a population mean with a margin of error $$E$$ and known standard deviation $$\sigma. $$Which formula should be used?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2} \sigma}{E} \$$right)^2$$

Question 13

Which non-parametric test is used to compare two independent samples when the data are not normally distributed?

Accepted Answer

Mann-Whitney U Test

Question 14

A company wants to test if the mean lifetime of their new batteries is greater than 500 hours. Which of the following is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: \mu = 500$$, H_a$$: \mu \u003e 500$$

Question 15

In a paired sample scenario, the test statistic for the mean difference is calculated as:

Accepted Answer

$$t = \frac{\bar{d}}{s_d / \sqrt{n}}$$

Question 16

Which of the following is NOT a requirement for the independent two-sample t-test?

Accepted Answer

Samples must be dependent

Question 17

A researcher is testing $$H_0$$: \mu = 16.7$$ against H_a$$: \mu 
eq 16.7$$ with $$\sigma = 6$$, $$\alpha = 0.05$$, and n = 100$. What is the critical value for a two-sided z-test?

Accepted Answer

$$\pm 1.96$$

Question 18

Which test is most appropriate for comparing the variances of two independent samples from normal populations?

Accepted Answer

F-test

Question 19

A study compares the mean scores of two groups of students using a non-parametric test. Which test should be used if the groups are independent?

Accepted Answer

Mann-Whitney U Test

Question 20

Which formula is used to calculate the pooled sample variance $$s_p^2$ for two samples?

Accepted Answer

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

Study Guide: Inferences for Means and Variances in Introductory Statistics

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