Q: A sample proportion test uses the formula $$z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}. If$$ $$p = 0.6$$, $$n = 200$$, and $$\hat{p} = 0.38$$, what is the denominator of the z-score formula?

$$\sqrt{\frac{0.6 \times 0.4}{200}}$$

Question 1

A researcher is testing whether the mean of a population is different from 50 using a significance level of $$\alpha = 0.05. $$The sample mean is 51.2, the population standard deviation is 5, and the sample size is 30. What is the correct null hypothesis ($$H_0) $$for this test?

Accepted Answer

$$H_0$$: \mu = 50$$

Question 2

Given a two-tailed hypothesis test with $$\alpha = 0.05$$, what is the critical z-value for rejection of the null hypothesis?

Accepted Answer

$$z = \pm 1.96$$

Question 3

A sample of 200 households finds that 76 households have made lifestyle changes due to escalating gas prices. If the null hypothesis is $$p = 0.6$$, what is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = 0.38$$

Question 4

Which formula is used to calculate the z-score for a sample mean when the population standard deviation is known?

Accepted Answer

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

Question 5

A university wants to show that the mean GPA of its honors graduates is greater than 3.5. The sample mean is 3.8, the sample standard deviation is 0.4, and the sample size is 28. What is the correct alternative hypothesis ($$H_a$$)?

Accepted Answer

$$H_a: \mu \u003e 3.5$$

Question 6

If the calculated z-score for a test statistic is $$-2.83$$ and the critical value for a left-tailed test at $$\alpha = 0.01 is$$ $$-2.33$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis

Question 7

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

Accepted Answer

Rejecting a true null hypothesis

Question 8

A hardware store advertises an average of $$\100$ per order. A sample of 60 orders has a mean of $$\$$96$$ and a standard deviation of $$\20$. What is the test statistic for testing if the average order is less than advertised?

Accepted Answer

$$z = \frac{96 - 100}{\frac{20}{\sqrt{60}}}$$

Question 9

In a right-tailed test with $$\alpha = 0.10$$, what is the critical z-value?

Accepted Answer

$$z = 1.28$$

Question 10

If the p-value for a hypothesis test is $$0.002$$ and $$\alpha = 0.01$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis

Question 11

A sample proportion test uses the formula $$z = \frac{\hat{p} - p}{\sqrt{\frac{p(1-p)}{n}}}. If$$ $$p = 0.6$$, $$n = 200$$, and $$\hat{p} = 0.38$$, what is the denominator of the z-score formula?

Accepted Answer

$$\sqrt{\frac{0.6 	imes 0.4}{200}}$$

Question 12

Which of the following is the correct interpretation of a significance level $$\alpha = 0.05$$?

Accepted Answer

There is a 5% chance of rejecting the null hypothesis when it is true.

Question 13

A test statistic is calculated as $$z = -1.2$$ for a two-tailed test. If the critical values are $$\pm 1.96$$, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis

Question 14

If a university wants to be 99% confident that the mean GPA of its honors graduates is greater than 3.5, what is the appropriate critical value for a right-tailed test?

Accepted Answer

$$z = 2.33$$

Question 15

Which of the following scenarios best describes when to use a one-tailed test?

Accepted Answer

When the research hypothesis predicts a specific direction of effect

Hypothesis Testing for One Sample: Study Notes

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