Question 1

A local politician claims that the mean prison time for car thieves is less than the required 4 years. A random sample of 80 convicted car thieves had a sample mean prison time of 3.5 years, with a population standard deviation of 1.25 years. At $$\alpha = 0.05$$, which of the following is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: \mu \geq 4$$

Question 2

A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5 days. A random sample of 28 teachers provided the following data: 0, 3, 6, 3, 3, 5, 4, 1, 7, 3, 1, 2, 3, 3, 2, 4, 2, 5, 2, 8, 3, 1, 2, 5, 3, 5, 1, 6. What is the alternative hypothesis for this test?

Accepted Answer

$$H_a: \mu \u003c 5$$

Question 3

A study claims that at least 18% of lower high school students are overweight. In a sample of 144 students, 25 were found to be overweight. At $$\alpha = 0.05$$, what is the correct test statistic formula for this proportion hypothesis test?

Accepted Answer

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

Question 4

A mathematics teacher compares test scores of students learning an algebraic concept using traditional methods and then using manipulatives. The same students are tested both times. What type of samples are these?

Accepted Answer

Dependent samples

Question 5

A study was conducted to determine if the mean salaries of elementary school teachers from two neighboring states are equal. A sample of 100 teachers from each state was randomly selected. The sample mean from the first state was $$29,400 with a population standard deviation of 2$$,300. The sample mean from the second state was $$30,800 with a population standard deviation of 2$$,100. What is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: \$$mu_1$$ = \$$mu_2$$

Question 6

A sports analyst claims that the mean batting average for teams in the American League is not equal to the mean batting average for teams in the National League. Which statistical test should be used to evaluate this claim, assuming population variances are equal and samples are independent?

Accepted Answer

Two-sample t-test

Question 7

A pharmaceutical company tests a new drug to lower cholesterol. Ten subjects are tested before and after taking the drug for 6 months. Which statistical test is most appropriate to determine if the drug lowers cholesterol?

Accepted Answer

Paired t-test

Question 8

In a survey of 800 general practitioners, 30% felt the government should control health care. If 2011 specialists felt differently, which test would you use to determine if there is a difference in proportions between the two groups?

Accepted Answer

Two-proportion z-test

Question 9

A sample of 80 car thieves had a mean prison time of 3.5 years with a population standard deviation of 1.25 years. What is the correct formula for the test statistic to evaluate if the mean prison time is less than 4 years?

Accepted Answer

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

Question 10

A pharmaceutical company tests a new drug to lower cholesterol. Ten subjects are tested before and after taking the drug for 6 months. What is the correct formula for the paired t-test statistic?

Accepted Answer

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

Question 11

A sports analyst claims that the mean batting average for teams in the American League is not equal to the mean batting average for teams in the National League. What is the correct alternative hypothesis for this test?

Accepted Answer

$$H_a: \mu_1$ 
eq \mu_2$

Question 12

A local school district claims that the number of school days missed by its teachers due to illness is below the national average of 5 days. Which of the following is the correct decision rule for a one-tailed test at $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0 if$$ $$p-$$value $$\u003c 0.05$$

Question 13

A mathematics teacher compares test scores of students learning an algebraic concept using traditional methods and then using manipulatives. What is the main reason these samples are considered dependent?

Accepted Answer

The same students are tested twice

Question 14

A study was conducted to determine if the mean salaries of elementary school teachers from two neighboring states are equal. Which formula should be used to calculate the test statistic for this two-sample test, assuming equal variances?

Accepted Answer

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

Question 15

In a survey of 800 general practitioners, 30% felt the government should control health care. If 2011 specialists felt differently, what is the correct null hypothesis for a two-proportion z-test?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Step-by-Step Guidance for College Statistics Hypothesis Testing Worksheet

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