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

Which formula is used to calculate the confidence interval for the mean of a population when the population standard deviation $$\sigma is $$known?

Accepted Answer

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

Question 3

A researcher is testing whether the mean weight of a sample of apples differs from 150g. The population standard deviation is unknown. Which test statistic should be used?

Accepted Answer

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

Question 4

In hypothesis testing, what is the probability of making a Type I error?

Accepted Answer

$$\alpha$$

Question 5

A hospital wants to compare the variances of recovery times between two treatments. Which test should be used?

Accepted Answer

F-test for equality of variances

Question 6

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

Accepted Answer

The population variances must be equal

Question 7

A scientist collects paired data on before-and-after cholesterol levels for the same patients. Which test is most appropriate to analyze the mean difference?

Accepted Answer

Paired t-test

Question 8

If the power of a test is $$0.994$$, what is the probability of a Type II error ($$\beta$$)?

Accepted Answer

$$0.006$$

Question 9

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 10

A confidence interval for the difference in means between two independent samples (with unequal variances) is calculated using which formula?

Accepted Answer

$$(\bar{x}_1 - \bar{x}_2) \pm t_{\alpha/2} \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 11

Which of the following statements about the Wilcoxon's Signed Rank Test is correct?

Accepted Answer

It requires the distribution of differences to be symmetric

Question 12

A researcher wants to estimate the mean height of a population with a margin of error of $$2 cm $$and a confidence level of $$95\%. $$The population standard deviation is $$6 cm. $$What is the minimum sample size required?

Accepted Answer

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

Question 13

Which test is appropriate for comparing the means of two dependent samples?

Accepted Answer

Paired t-test

Question 14

In a hypothesis test, if the p-value is less than the significance level $$\alpha$$, what should you do?

Accepted Answer

Reject the null hypothesis

Question 15

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

Accepted Answer

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

Question 16

A Type II error occurs when:

Accepted Answer

The null hypothesis is not rejected when it is false

Question 17

Which test is used to compare the medians of two independent samples when the data are not normally distributed?

Accepted Answer

Mann-Whitney U Test

Question 18

A confidence interval for the mean difference in paired samples is given by:

Accepted Answer

$$\bar{d} \pm t_{\alpha/2} \frac{s_d}{\sqrt{n}}$$

Question 19

Which of the following is NOT a requirement for the F-test for comparing two variances?

Accepted Answer

Samples must be dependent

Question 20

A researcher uses the Wilcoxon's Signed Rank Test for paired data. What is the main assumption about the distribution of differences?

Accepted Answer

The distribution of differences is symmetric

Study Guide: Inferences for Means and Variances in Introductory Statistics

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