Question 1

A pharmaceutical company wants to compare the effectiveness of two drugs in lowering blood pressure. They randomly assign 40 patients to Drug A and 35 patients to Drug B. The sample means and standard deviations are $$\bar{x}_1 = 8$$, $$s_1 = 2$ for Drug A, and $$\bar{x}_2 = 6$$, s_2$ = 3$$ for Drug B. Which formula should be used to calculate the test statistic for testing $$H_0$$: \$$mu_1$$ - \$$mu_2 = 0$ if the variances are assumed unequal?

Accepted Answer

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

Question 2

Which of the following is an assumption for conducting a one-sample $$t-$$test for the mean with unknown standard deviation?

Accepted Answer

The sample data are drawn from a nearly Normal distribution.

Question 3

A researcher wants to test if the proportion of smokers in a city is different from the national average of 20%. In a random sample of 150 people, 36 are smokers. What is the correct test statistic formula for this hypothesis test?

Accepted Answer

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

Question 4

Which of the following is NOT an assumption for the Chi-Square Goodness of Fit test?

Accepted Answer

The data must be measured on an interval scale.

Question 5

A hospital wants to compare the recovery times of patients before and after a new treatment using paired data. Which test statistic should be used?

Accepted Answer

$$t = \dfrac{\bar{d} - \mu_0$}{s_d/\sqrt{n}}$$

Question 6

Which formula gives the margin of error for a confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

$$ME = z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}$$

Question 7

A company wants to estimate the sample size needed to estimate a population proportion with a margin of error of 0.03 at 95% confidence. Which formula should they use?

Accepted Answer

$$n = \left( \dfrac{z_{\alpha/2} \sqrt{\hat{p}(1-\hat{p})}}{ME} \$$right)^2$$

Question 8

Which test would be most appropriate to compare the median of a non-Normal population to a hypothesized value?

Accepted Answer

Wilcoxon Signed-Rank Test

Question 9

A researcher is comparing two independent samples with reasonably symmetric but non-Normal distributions. Which test should be used to compare their central tendencies?

Accepted Answer

Mann-Whitney U (Wilcoxon Sum Rank) Test

Question 10

Which of the following is the correct formula for the pooled variance $$s_p^2$ when conducting a two-sample t$-test with equal variances?

Accepted Answer

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

Question 11

A study is testing $$H_0$$: $$p_1$$ - $$p_2 = 0$ for two proportions using pooled variance. What is the formula for the pooled proportion $$\bar{p}$$?

Accepted Answer

$$\bar{p} = \dfrac{x_1$ + x_2$}{n_1$ + n_2$}$$

Question 12

Which of the following is the correct test statistic for a Chi-Square test of independence?

Accepted Answer

$$\$$chi^2$$_{stat} = \sum \dfrac{(Obs - $$Exp)^2$$}{Exp}$$

Question 13

A scientist wants to construct a one-sided lower bound confidence interval for a mean. Which formula should be used?

Accepted Answer

$$(Estimate - z_{\alpha} 	imes SD, \infty) or$$ $$(Estimate - t_{\alpha, df} 	imes SE, \infty)$$

Question 14

Which of the following is a correct decision rule for a two-tailed $$t-$$test at significance level $$\alpha$$?

Accepted Answer

$$|t_{stat}| \u003e t_{\alpha/2, df}$$

Question 15

A quality control manager wants to test if the median weight of a product batch differs from 500g, but the data are not Normally distributed. Which test should be used?

Accepted Answer

Wilcoxon Signed-Rank Test

Question 16

Which of the following is an assumption for the Mann-Whitney U (Wilcoxon Sum Rank) test?

Accepted Answer

The two samples are independent and drawn from reasonably symmetric distributions.

Question 17

A researcher is testing $$H_0$$: \mu = 100$$ using a sample mean $$\bar{x} = 104$$, sample standard deviation s = 8$, and n = 16$. What is the value of the test statistic?

Accepted Answer

$$t = \dfrac{104 - 100}{8/\sqrt{16}} = 2$$

Question 18

Which of the following is the correct formula for the standard error of the difference between two independent sample means with equal variances?

Accepted Answer

$$SE = s_p \sqrt{\dfrac{1}{n_1$} + \dfrac{1}{n_2$}}$$

Hypothesis Testing and Confidence Intervals: Formula Sheet Study Guide

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