Q: According to a Pew Research Centre Survey, 15% of adults are cord-cutters. In a random sample of 500 adults, what is the standard error of the sample proportion ($$\hat{p}$$)?

Standard error is $$\sqrt{\frac{0.15 \times 0.85}{500}}$$

Q: You want to estimate the mean resale value of a 5-year-old foreign sedan. From a sample of 17 cars, the mean resale price is $$13,800 and the standard deviation is 600. $$What is the correct formula for the 95% confidence interval for the true mean?

Confidence interval: $$13,800 \pm t_{0.025,16} \times \frac{600}{\sqrt{17}}$$

Q: The U.S. Commission on Crime finds 380 out of 600 crimes involved a firearm. What is the formula for the 90% confidence interval for the true proportion $$p$$?

Confidence interval: $$\hat{p} \pm z_{0.05} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{600}}$$

Q: For the breast cancer screening test, what is the formula for the test statistic to compare the new method to the old?

$$z = \frac{\hat{p} - 0.15}{\sqrt{0.15 \times 0.85 / 70}}$$

Q: If a sample proportion $$\hat{p} is 0.12 $$from a sample of 500, and the population proportion $$p is 0.15$$, what is the z-score formula to test if $$\hat{p} is $$significantly less than $$p$$?

$$z = \frac{0.12 - 0.15}{\sqrt{0.15 \times 0.85 / 500}}$$

Question 1

A random sample of 45 senior managers has an average level of support for corporate sustainability (x̄) of 68, with a population mean of 68 and standard deviation of 27. What is the probability that the sample mean x̄ is greater than 65? Use the Central Limit Theorem and provide the formula for the z-score.

Accepted Answer

The probability is calculated using $$z = \frac{65 - 68}{27 / \sqrt{45}}$$

Question 2

According to a Pew Research Centre Survey, 15% of adults are cord-cutters. In a random sample of 500 adults, what is the standard error of the sample proportion ($$\hat{p}$$)?

Accepted Answer

Standard error is $$\sqrt{\frac{0.15 	imes 0.85}{500}}$$

Question 3

You want to estimate the mean resale value of a 5-year-old foreign sedan. From a sample of 17 cars, the mean resale price is $$13,800 and the standard deviation is 600. $$What is the correct formula for the 95% confidence interval for the true mean?

Accepted Answer

Confidence interval: $$13,800 \pm t_{0.025,16} 	imes \frac{600}{\sqrt{17}}$$

Question 4

The U.S. Commission on Crime finds 380 out of 600 crimes involved a firearm. What is the formula for the 90% confidence interval for the true proportion $$p$$?

Accepted Answer

Confidence interval: $$\hat{p} \pm z_{0.05} 	imes \sqrt{\frac{\hat{p}(1-\hat{p})}{600}}$$

Question 5

A revenue department wants to test if the average time to fill out pension form ABC-5500 has decreased from 63 hours. A sample of 72 owners has a mean of 62.7 hours and standard deviation of 20 hours. What are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: \mu = 63$$, H_a$$: \mu \u003c 63$$

Question 6

For the pension form completion time test, what is the formula for the test statistic?

Accepted Answer

$$z = \frac{62.7 - 63}{20 / \sqrt{72}}$$

Question 7

A sample of 8 measurements from a normal population has $$\bar{x} = 5.2$$, $$s = 1.1. $$Test $$H_0$$: \mu = 4$$ vs H_a$$: \mu 
eq 4$$ at $$\alpha = 0.05$$. What is the formula for the test statistic?

Accepted Answer

$$t = \frac{5.2 - 4}{1.1 / \sqrt{8}}$$

Question 8

A new breast cancer screening method failed to detect cancer in 8 out of 70 women known to have the disease. The old method failed in 15% of cases. What is the correct null hypothesis for this test?

Accepted Answer

$$H_0$$: p = 0.15$$

Question 9

For the breast cancer screening test, what is the formula for the test statistic to compare the new method to the old?

Accepted Answer

$$z = \frac{\hat{p} - 0.15}{\sqrt{0.15 	imes 0.85 / 70}}$$

Question 10

In hypothesis testing, what does the rejection region represent?

Accepted Answer

The set of values for the test statistic that leads to rejection of the null hypothesis

Question 11

If a sample proportion $$\hat{p} is 0.12 $$from a sample of 500, and the population proportion $$p is 0.15$$, what is the z-score formula to test if $$\hat{p} is $$significantly less than $$p$$?

Accepted Answer

$$z = \frac{0.12 - 0.15}{\sqrt{0.15 	imes 0.85 / 500}}$$

Question 12

When constructing a confidence interval for a mean with a small sample size ($$n \u003c 30) $$and unknown population standard deviation, which distribution should be used?

Accepted Answer

The t-distribution

Question 13

A sample of 17 cars has a mean resale value of $$13,800 and standard deviation of 600. $$What is the margin of error for a 95% confidence interval?

Accepted Answer

$$t_{0.025,16} 	imes \frac{600}{\sqrt{17}}$$

Question 14

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 15

For a sample mean test with $$n = 72$$, sample mean $$= 62.7$$, population mean $$= 63$$, and sample standard deviation $$= 20$$, what is the value of the test statistic?

Accepted Answer

$$z = \frac{62.7 - 63}{20 / \sqrt{72}} \approx -0.12$$

Question 16

A sample of 8 measurements has $$\bar{x} = 5.2$$, $$s = 1.1$$, and the null hypothesis is $$\mu = 4. $$What is the calculated t-statistic?

Accepted Answer

$$t = \frac{5.2 - 4}{1.1 / \sqrt{8}} \approx 2.92$$

Question 17

In a sample of 70 women, 8 failed detections occurred. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \frac{8}{70} \approx 0.114$$

Question 18

If the calculated z-score for a hypothesis test is outside the rejection region, what is the correct conclusion?

Accepted Answer

Fail to reject the null hypothesis

Statistics Word Problems – Step-by-Step Guidance for Financial-Accounting Students

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