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

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