Q: A researcher wants to test if the average time spent on phone calls has changed from 42.8 minutes per day. Which of the following is the correct set of hypotheses?

$$H_0$$: \mu = 42.8$$; H_a$$: \mu \neq 42.8$$

Question 1

Which of the following best describes the null hypothesis ($$H_0) in a $$hypothesis test for a single population mean?

Accepted Answer

$$H_0$$: \mu = \$$mu_0$$

Question 2

A researcher wants to test if the average time spent on phone calls has changed from 42.8 minutes per day. Which of the following is the correct set of hypotheses?

Accepted Answer

$$H_0$$: \mu = 42.8$$; H_a$$: \mu 
eq 42.8$$

Question 3

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

Accepted Answer

Rejecting the null hypothesis when it is actually true

Question 4

A 95% confidence interval for the difference in proportions between two groups is $$(-0.08, 0.05). $$What does this interval suggest?

Accepted Answer

There is no significant difference between the two proportions at the 0.05 significance level

Question 5

Which of the following is the correct formula for the test statistic in a one-sample $$z-$$test for a population mean when the population standard deviation is known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\sigma / \sqrt{n}}$$

Question 6

A baseball analyst uses the regression equation $$\hat{y} = 5x + 100 to $$predict the distance a ball travels ($$y) $$based on its speed ($$x). $$What does the slope of 5 represent?

Accepted Answer

For each 1 mph increase in speed, the predicted distance increases by 5 feet

Question 7

If a $$p-$$value is 0.03 and the significance level $$\alpha is 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis; there is sufficient evidence to support the alternative hypothesis

Question 8

Which of the following is an assumption for performing a two-sample $$t-$$test for independent means?

Accepted Answer

The two samples are independent of each other

Question 9

A study finds a $$p-$$value of 0.12 when testing whether the mean time spent on social media differs from 2 hours per day. What is the correct interpretation at $$\alpha = 0.05$$?

Accepted Answer

There is not enough evidence to conclude that the mean time differs from 2 hours per day

Question 10

Which TI-84 Plus CE function would you use to test the difference between two independent means?

Accepted Answer

2-SampTTest

Question 11

A 95% confidence interval for the mean difference in exam scores between two semesters is $$(1.5, 8.0). $$What does this interval suggest?

Accepted Answer

The mean exam score in the first semester is significantly higher than in the second semester

Question 12

Which of the following is the correct formula for the standard error of the difference between two independent sample proportions $$\hat{p}_1$$ and $$\hat{p}_2$$?

Accepted Answer

$$SE = \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1$} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2$}}$$

Question 13

A researcher wants to know if the mean commute time in Houston is different from the national mean of 25 minutes. Which test should be used?

Accepted Answer

One-sample $$t-$$test for the mean

Question 14

In a regression analysis, the $$R^2$$ value is 0.85. What does this indicate?

Accepted Answer

85% of the variation in the response variable is explained by the model

Question 15

Which of the following is NOT an assumption for performing a hypothesis test for a single population mean?

Accepted Answer

The sample size must be less than 10

Question 16

A 95% confidence interval for the mean number of hours spent on homework per week is $$(6.2, 8.4). $$Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the true mean number of hours spent on homework per week is between 6.2 and 8.4

Question 17

Which of the following scenarios would require a paired $$t-$$test?

Accepted Answer

Comparing the test scores of students before and after using an online homework system

Question 18

A sample of 100 students has a mean exam score of 78 with a standard deviation of 10. What is the 95% confidence interval for the mean exam score? (Use $$z^* = 1.96)$$

Accepted Answer

$$78 \pm 1.96 	imes \frac{10}{\sqrt{100}}$$

Question 19

Which of the following best describes the alternative hypothesis ($$H_a) in a $$two-tailed test for a population proportion?

Accepted Answer

$$H_a: p 
eq p_0$

Exam 4 Review: Hypothesis Testing, Confidence Intervals, and Regression

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