Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A survey asks high school students to report how often they consume alcoholic drinks. Which type of bias is most likely present in this scenario?

Accepted Answer

Volunteer bias

Question 3

Which of the following is NOT a property of the standard normal distribution (SND)?

Accepted Answer

The distribution is skewed to the right.

Question 4

Suppose the area to the left of $z = 1.28$ under the standard normal curve is 0.8997. What is the area to the right of $z = 1.28$?

Accepted Answer

$0.1003$

Question 5

If a 95% confidence interval for a population proportion is $(0.587, 0.648)$, what is the point estimate for the population proportion?

Accepted Answer

$0.6175$

Question 6

Which formula is used to calculate the margin of error for a confidence interval for a population proportion?

Accepted Answer

$E = z_{\alpha/2} \sqrt{\frac{\hat{p}\hat{q}}{n}}$

Question 7

A local magazine reports that 61% of Americans use Spotify as their primary app to stream music. A random sample of 300 Americans found that 215 use Spotify. What is the sample proportion?

Accepted Answer

$0.72$

Question 8

Which of the following is the correct null hypothesis ($H_0$) for testing if the true proportion of students who graduate within 3 years at a college is 70%?

Accepted Answer

$H_0: p = 0.70$

Question 9

Which of the following would decrease the margin of error in a confidence interval for a population proportion, assuming all other factors remain constant?

Accepted Answer

Increasing the sample size

Question 10

A Type I error in hypothesis testing occurs when:

Accepted Answer

The null hypothesis is rejected when it is true.

Question 11

Given $n = 100$, $\hat{p} = 0.6$, and $z_{\alpha/2} = 1.96$, what is the margin of error for a 95% confidence interval for the population proportion?

Accepted Answer

$0.096$

Question 12

Which of the following is a requirement for using the normal approximation to the binomial distribution for sample proportions?

Accepted Answer

Both $np$ and $nq$ are greater than 5.

Question 13

If the level of significance ($\alpha$) is increased in a hypothesis test, what happens to the critical value $z_{\alpha/2}$?

Accepted Answer

It decreases.

Question 14

A researcher wants to estimate the proportion of voters who support a new policy with 95% confidence and a margin of error of 3%. What is the minimum sample size required if no preliminary estimate is available?

Accepted Answer

$n = \left( \frac{z_{\alpha/2}}{E} \right)^2 \cdot 0.25$

Question 15

Which of the following best describes the meaning of a 95% confidence interval for a population proportion?

Accepted Answer

If we took many samples, about 95% of the calculated intervals would contain the true population proportion.

Question 16

A Type II error in hypothesis testing occurs when:

Accepted Answer

The null hypothesis is not rejected when it is false.

Question 17

Which of the following scenarios is most likely to result in nonresponse bias?

Accepted Answer

A survey is mailed to 1,000 people, but only 200 respond.

Question 18

If the area to the left of $z$ is 0.025, what is the value of $z$?

Accepted Answer

$z = -1.96$

Question 19

Which of the following is the correct formula for the test statistic when testing a claim about a population proportion?

Accepted Answer

$z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}}$

MTH161: Review of Statistics I – Core Concepts and Applications

Study Guide - Practice Questions

Study Guide - Flashcards