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

Study Guide - Practice Questions

Study Guide - Flashcards