Question 1

A researcher wants to estimate the proportion of employees at a company who prefer remote work. In a random sample of 250 employees, 92 indicate a preference for remote work. Construct a 95% confidence interval for the true proportion of employees who prefer remote work. Which formula should be used?

Accepted Answer

$$ \hat{p} \pm z_{\alpha/2} \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}} $$

Question 2

Which of the following best describes the null hypothesis ($$H_0) in a $$test comparing the mean heights of male and female students?

Accepted Answer

$$ H_0$: \mu_{male} = \mu_{female} $$

Question 3

A sociologist measures attitudes towards public transportation. The mean score from 27 subjects is 76.2 with a standard deviation of 8.2. What is the correct formula for a 99% confidence interval for the mean?

Accepted Answer

$$ \bar{x} \pm t_{\alpha/2} \dfrac{s}{\sqrt{n}} $$

Question 4

A sample of 147 children finds that 37 of them suffer from asthma. Test the claim that the proportion of children in the area who suffer from asthma is less than 0.30 at the 0.01 significance level. What is the alternative hypothesis ($$H_a$$)?

Accepted Answer

$$ H_a: p \u003c 0.30 $$

Question 5

Which of the following is the correct formula to calculate the minimum sample size required to estimate a population proportion with margin of error $$E$$, confidence level $$1-\alpha$$, and estimated proportion $$\hat{p}$$?

Accepted Answer

$$ n = \dfrac{z_{\alpha/2}^2 \hat{p}(1-\hat{p})}{E^2$} $$

Question 6

A business student wants to estimate the mean monthly rent paid by students. The population standard deviation is known to be $$\87.1$. What formula should be used to determine the minimum sample size required to estimate the mean with a margin of error E$ and confidence level 1$$-\alpha$?

Accepted Answer

$$ n = \left( \dfrac{z_{\alpha/2} \sigma}{E} \$$right)^2$$ $$

Question 7

In hypothesis testing, what does the P-value represent?

Accepted Answer

The probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.

Question 8

A consumer advocacy group tests the claim that an oil change shop completes oil changes in under 15 minutes. A sample of 10 customers yields a mean time of 13.8 minutes and a sample standard deviation of 1.73 minutes. What is the correct test statistic formula for this hypothesis test?

Accepted Answer

$$ t = \dfrac{\bar{x} - \mu_0$}{s / \sqrt{n}} $$

Question 9

Which of the following statements about the rejection region in hypothesis testing is correct?

Accepted Answer

It is the set of values for the test statistic that leads to rejection of the null hypothesis.

Question 10

A researcher wants to test if the mean commute time for a city is greater than 30 minutes. Which of the following is the correct alternative hypothesis?

Accepted Answer

$$ H_a: \mu \u003e 30 $$

Question 11

If a 95% confidence interval for a population mean is $$(67.7, 82.7)$$, what does this mean in context?

Accepted Answer

We are 95% confident that the true population mean lies between 67.7 and 82.7.

Question 12

Which of the following is a correct interpretation if the P-value in a hypothesis test is less than the significance level $$\alpha$$?

Accepted Answer

Reject the null hypothesis.

Question 13

A test statistic is calculated as $$z = -2.77$$ for a left-tailed test. The critical value is $$z_{\alpha} = -2.33. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following is NOT required when conducting a hypothesis test for a population mean with unknown standard deviation?

Accepted Answer

Population standard deviation $$\sigma$$

Question 15

A sample of 43 male students has a mean height of 69.2 inches and a standard deviation of 2.8 inches. What is the correct formula for the 95% confidence interval for the mean height?

Accepted Answer

$$ \bar{x} \pm t_{\alpha/2} \dfrac{s}{\sqrt{n}} $$

Question 16

In a right-tailed hypothesis test, which of the following would be considered evidence against the null hypothesis?

Accepted Answer

A test statistic greater than the critical value.

Question 17

Which of the following is the correct formula for the test statistic in a hypothesis test for a population proportion?

Accepted Answer

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

Question 18

A 99% confidence interval for a population mean is wider than a 95% confidence interval for the same data. Why?

Accepted Answer

A higher confidence level requires a larger margin of error.

Confidence Intervals, Hypothesis Testing, and Sample Size Estimation: Study Notes

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