Question 1

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

Accepted Answer

A point estimate is a single value that best describes the population of interest.

Question 2

Suppose the Bureau of Labor Statistics (BLS) reports a sample unemployment rate of 3.8% with a 95% confidence interval of (3.65%, 3.95%). What does this interval mean?

Accepted Answer

We are 95% confident that the true population unemployment rate is between 3.65% and 3.95%.

Question 3

Which formula is used to calculate the standard error of the mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$$

Question 4

A company wants to estimate the average online order size for its customers. The sample mean is $$129.20$$, the population standard deviation is $$40.60$$, and the sample size is $$32. $$What is the standard error of the mean?

Accepted Answer

$$\frac{40.60}{\sqrt{32}} = 7.173$$

Question 5

If you increase the confidence level from 90% to 99%, what happens to the width of the confidence interval?

Accepted Answer

The confidence interval gets wider.

Question 6

Which formula gives the upper confidence limit (UCL) for the mean when the population standard deviation is known?

Accepted Answer

$$UCL_{\bar{x}} = \bar{x} + z_{\alpha/2} \sigma_{\bar{x}}$$

Question 7

When the population standard deviation is unknown, which distribution should be used to construct a confidence interval for the mean?

Accepted Answer

Student's t-distribution

Question 8

A sample of 18 patients has a mean weekly visit of 103 and a sample standard deviation of 10.6. What is the margin of error for a 95% confidence interval using Excel's CONFIDENCE.T function?

Accepted Answer

$$CONFIDENCE.T(0.05, 10.6, 18) = 8.25$$

Question 9

Which condition must be met to use the normal distribution to approximate the binomial distribution when constructing a confidence interval for a proportion?

Accepted Answer

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

Question 10

A bank wants to estimate the proportion of households without a checking account. In a pilot sample of 50 households, 6 did not have a checking account. What is the sample proportion?

Accepted Answer

$$\frac{6}{50} = 0.12$$

Question 11

Which formula is used to calculate the sample size needed to estimate a population mean with a specified margin of error $$ME$$?

Accepted Answer

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

Question 12

Why is setting $$p = 0.5$$ used when estimating the required sample size for a population proportion if no pilot sample is available?

Accepted Answer

It provides the most conservative (largest) estimate for the sample size.

Question 13

Which formula adjusts the standard error for a finite population when estimating the mean?

Accepted Answer

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

Question 14

A university has 1,600 business students. A sample of 100 students has a mean of 7,277 steps per day and a standard deviation of 1,480. What is the finite population correction factor?

Accepted Answer

$$\sqrt{\frac{1600-100}{1600-1}}$$

Question 15

Which of the following is a common mistake when interpreting a confidence interval?

Accepted Answer

Saying there is a 90% probability that the population mean is within the interval.

Question 16

If the sample size increases while all other factors remain constant, what happens to the margin of error of a confidence interval?

Accepted Answer

The margin of error decreases.

Question 17

A sample of 15 households has an average credit card debt of $$8,150$$ and a population standard deviation of $$2,970. $$What is the standard error of the mean?

Accepted Answer

$$\frac{2,970}{\sqrt{15}} = 767.44$$

Question 18

Which formula is used to calculate the confidence interval for a proportion?

Accepted Answer

$$UCL_p = \hat{p} + z_{\alpha/2} \sigma_{\hat{p}}$$

Chapter 8: Confidence Intervals – Business Statistics Study Notes

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