Question 1

Which of the following is NOT a required condition for constructing a confidence interval for a population proportion?

Accepted Answer

The variable is quantitative.

Question 2

A researcher wants to estimate the average number of hours college students sleep per night. Which of the following conditions must be met to use the normal distribution for the sampling distribution of the sample mean?

Accepted Answer

The sample size is at least 30 or the population is normally distributed.

Question 3

Suppose you have a sample proportion $$\hat{p} = 0.4$$ from a sample of $$n = 100. $$What is the mean of the sampling distribution of the sample proportion if the population proportion is $$p = 0.5$$?

Accepted Answer

$$0.5$$

Question 4

Which formula gives the standard deviation of the sampling distribution of the sample mean?

Accepted Answer

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

Question 5

A 95% confidence interval for a population mean is $$(12.4, 15.6). $$What is the point estimate for the population mean?

Accepted Answer

$$14.0$$

Question 6

Which of the following best describes what a 99% confidence interval means?

Accepted Answer

If we repeated the sampling process many times, about 99% of the intervals would contain the true population parameter.

Question 7

A pharmaceutical company wants to estimate the proportion of patients who experience side effects from a new drug. They want the margin of error to be no more than 0.03 at a 95% confidence level. Which formula should they use to determine the minimum sample size required?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2}}{E} \$$right)^2$$ p(1-p)$$

Question 8

Which of the following statements is TRUE regarding the effect of increasing the confidence level on the width of a confidence interval?

Accepted Answer

Increasing the confidence level increases the width of the confidence interval.

Question 9

A hospital administrator wants to test if the average wait time in the emergency room is greater than 30 minutes. Which is the correct set of hypotheses for this test?

Accepted Answer

$$H_0$$: \mu = 30$$; H_a$$: \mu \u003e 30$$

Question 10

In a hypothesis test for a population proportion, which formula is used to calculate the test statistic $$z_0$$?

Accepted Answer

$$z_0$$ = \frac{\hat{p} - $$p_0$$}{\sqrt{\frac{$$p_0(1$$-$$p_0$$)}{n}}}$$

Question 11

A sample of 50 patients has a mean cholesterol level of 190 mg/dL with a sample standard deviation of 20 mg/dL. What is the correct formula for the 95% confidence interval for the population mean?

Accepted Answer

$$\bar{x} \pm t_{\alpha/2, n-1} \cdot \frac{s}{\sqrt{n}}$$

Question 12

If the p-value in a hypothesis test is 0.03 and the significance level $$\alpha is 0.05$$, what is the correct decision?

Accepted Answer

Reject the null hypothesis.

Question 13

A study finds a 90% confidence interval for the proportion of defective products is $$(0.02, 0.08). $$What is the margin of error?

Accepted Answer

$$0.03$$

Question 14

Which of the following is a correct interpretation of a p-value?

Accepted Answer

The probability of observing a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.

Question 15

A sample of 200 people is surveyed, and 60 say they prefer brand A. What is the sample proportion $$\hat{p}$$?

Accepted Answer

$$0.3$$

Question 16

Which of the following is NOT a condition for using the sampling distribution of the sample mean?

Accepted Answer

The variable is qualitative.

Question 17

A researcher wants to test if the proportion of smokers in a city is less than 20%. Which is the correct alternative hypothesis?

Accepted Answer

$$H_a: p \u003c 0.20$$

Question 18

Which of the following scenarios would be considered 'unusual' based on probability?

Accepted Answer

A probability less than 0.05.

Question 19

A sample of 36 students has a mean test score of 82 and a standard deviation of 6. What is the standard error of the mean?

Accepted Answer

$$1$$

Question 20

If you want to decrease the width of a confidence interval for a population mean, which of the following should you do?

Accepted Answer

Increase the sample size.

Sampling Distributions, Confidence Intervals, and Hypothesis Testing: Study Guide

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