Question 1

A researcher wants to estimate the average time (in minutes) it takes students to complete a statistics exam. She collects a random sample of 40 students and calculates a sample mean of 55 minutes with a sample standard deviation of 8 minutes. Which formula should she use to construct a 95% confidence interval for the population mean?

Accepted Answer

Use the t-value formula: $$\boxed{\bar{x} \pm t^* \frac{s}{\sqrt{n}}}$$

Question 2

A medical study compares the percentage of patients who recover from a treatment in two hospitals. Hospital A: 60 out of 100 recover; Hospital B: 70 out of 120 recover. Which statistical test should be used to compare the recovery proportions?

Accepted Answer

Two-sample z-test for proportions

Question 3

A researcher tests whether a new teaching method increases average test scores. The null hypothesis is $$H_0$$: \mu = 75$$ and the alternative is H_1$: \mu \u003e 75. If $$the p-value is 0.03 and $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject $$H_0$$; there is sufficient evidence the method increases scores.

Question 4

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting $$H_0$$ when $$H_0 is $$true

Question 5

A study measures cholesterol levels in patients before and after a new diet. Which statistical procedure is most appropriate?

Accepted Answer

Matched-pairs t-test for dependent samples

Question 6

A confidence interval for the difference in means between two independent groups is calculated as $$(-2.5, 4.7). $$What does this interval suggest?

Accepted Answer

There is no significant difference between the two group means.

Question 7

Which formula is used to calculate the test statistic for comparing two independent sample means?

Accepted Answer

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

Question 8

A researcher constructs 300 confidence intervals at the 90% confidence level. How many intervals are expected to contain the true parameter?

Accepted Answer

270

Question 9

Which of the following statements about confidence intervals is TRUE?

Accepted Answer

A 99% confidence interval is wider than a 95% confidence interval.

Question 10

In a hypothesis test, the probability of a Type I error is:

Accepted Answer

$$\alpha$$

Question 11

A survey asks whether the proportion of remote workers in New Jersey is different from New York. Which hypothesis symbols should be used?

Accepted Answer

$$H_1$$: p_{NJ} 
eq p_{NY}$$

Question 12

Which scenario describes an observational study?

Accepted Answer

Researchers observe and record the eating habits of students without intervention.

Question 13

A test statistic is calculated as $$t = 2.60$$ and the critical value is $$t = 1.75$$ for a right-tailed test. What is the correct decision?

Accepted Answer

Reject $$H_0$$; there is sufficient evidence for $$H_1.$$

Question 14

Which formula is used to calculate the margin of error for a confidence interval for a population proportion?

Accepted Answer

$$\boxed{z^* 	imes \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}}$$

Question 15

A study compares the average commute times for two cities using random samples of 35 people from each city. Which test should be used?

Accepted Answer

Two-sample t-test for independent means

Question 16

If the confidence interval for a proportion does NOT contain the old proportion, what does this indicate?

Accepted Answer

There is evidence of change.

Question 17

Which formula is used to calculate the test statistic for matched-pairs (dependent samples) data?

Accepted Answer

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

Question 18

Which of the following is TRUE about the power of a statistical test?

Accepted Answer

Power is equal to $$1 - \beta$$, where $$\beta is $$the probability of a Type II error.

Question 19

A study finds that the sample mean for group A is 45 and for group B is 42. If the confidence interval for $$\mu_A - \mu_B is$$ $$(0.5, 5.5)$$, what can be concluded?

Accepted Answer

Group A has a significantly higher mean than group B.

Hypothesis Testing, Confidence Intervals, and Two-Sample Inference: Exam Study Guide

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