Question 1

Which of the following best describes a point estimate in statistics?

Accepted Answer

A single value that best describes the population of interest.

Question 2

Suppose you want to construct a 95% confidence interval for the mean when the population standard deviation $$\sigma is $$known and the sample size $$n \geq 30. $$Which formula should you use for the upper confidence limit (UCL)?

Accepted Answer

$$UCL_{\overline{x}} = \overline{x} + z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}$$

Question 3

A sample of 32 online orders at Gap has a mean of $$129.20 and a population standard deviation of 40.60. $$What is the standard error of the mean?

Accepted Answer

$$\sigma_{\overline{x}} = \dfrac{40.60}{\sqrt{32}} = 7.173$$

Question 4

If you increase the confidence level from 90% to 99%, what happens to the width of the confidence interval for the mean (assuming all else is constant)?

Accepted Answer

The confidence interval becomes wider.

Question 5

Which of the following is the correct formula for the margin of error (ME) for a confidence interval for the mean when $$\sigma is $$known?

Accepted Answer

$$ME_{\overline{x}} = z_{\alpha/2} \dfrac{\sigma}{\sqrt{n}}$$

Question 6

A random sample of 15 households has an average credit card debt of $$8,150. The population standard deviation is 2$$,970. What is the 99% confidence interval for the population mean?

Accepted Answer

$$6,173.84 to$$ $$10,126.16$$

Question 7

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

Accepted Answer

Student’s t-distribution

Question 8

Which formula gives the sample size needed to estimate a population mean with a specified margin of error $$ME_{\overline{x}}$$ and confidence level (when $$\sigma is $$known)?

Accepted Answer

$$n = \dfrac{(z_{\alpha/2})^2$ \$$sigma^2$$}{(ME_{\overline{x}})^2$}$$

Question 9

A company wants to estimate the proportion of customers who prefer free shipping. In a sample of 200 customers, 80 prefer free shipping. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$\hat{p} = \dfrac{80}{200} = 0.40$$

Question 10

Which of the following conditions must be met to use the normal approximation for a confidence interval for a proportion?

Accepted Answer

$$np \geq 5$$ and $$n(1-p) \geq 5$$

Question 11

A survey of 1,163 people finds that 38.2% prefer football. If the 95% confidence interval for this proportion is (0.35, 0.41), how should this interval be interpreted?

Accepted Answer

We are 95% confident that the true proportion of people who prefer football is between 0.35 and 0.41.

Question 12

Which formula should be used to calculate the confidence interval for a population proportion?

Accepted Answer

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

Question 13

A finite population correction factor is needed when:

Accepted Answer

The sample size is a significant fraction of the population size.

Question 14

Which formula represents the finite population correction factor?

Accepted Answer

$$\sqrt{\dfrac{N-n}{N-1}}$$

Question 15

If a 95% confidence interval for the mean number of steps per day for a finite population is (6,992.6, 7,561.4), and the national average is 6,886, what can you conclude?

Accepted Answer

The population mean for this group is likely higher than the national average.

Question 16

Which Excel function would you use to find the critical t-score for a two-tailed confidence interval?

Accepted Answer

=T.INV.2T(alpha, degrees_freedom)

Question 17

A business wants to estimate the average monthly data usage of its customers with a margin of error of ±75 MB at 95% confidence. If $$\sigma = 400 MB $$and $$z_{0.025} = 1.96$$, what sample size is required?

Accepted Answer

$$n = \dfrac{(1.96)^2$ (400)^2$}{(75)^2$} = 109.3 \approx 110$$

Question 18

Which of the following statements about the t-distribution is TRUE?

Accepted Answer

The t-distribution is flatter and wider than the normal distribution.

Chapter 8: Confidence Intervals – Business Statistics Study Notes

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