Q: A poll finds that 60% of a random sample of 150 voters support a new policy. What is the standard error of the sample proportion?

$$\sqrt{\frac{0.6 \times 0.4}{150}}$$

Question 1

Which of the following best describes a 'parameter' in statistics?

Accepted Answer

A numerical summary describing a population.

Question 2

Suppose a researcher collects data from 200 randomly selected college students to estimate the average number of hours spent studying per week. What is the sample in this scenario?

Accepted Answer

The 200 randomly selected college students.

Question 3

Which formula is used to calculate the standard error for a sample proportion?

Accepted Answer

$$\sqrt{\frac{p(1-p)}{n}}$$

Question 4

A poll finds that 60% of a random sample of 150 voters support a new policy. What is the standard error of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.6 	imes 0.4}{150}}$$

Question 5

According to the Central Limit Theorem, which condition must be met for the sampling distribution of the sample proportion to be approximately normal?

Accepted Answer

$$np \u003e 10$$ and $$n(1-p) \u003e 10$$

Question 6

You want to find a 95% confidence interval for the proportion of defective items in a factory. If your sample proportion is $$\hat{p} = 0.08$$ and $$n = 500$$, which formula should you use?

Accepted Answer

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 7

A hospital administrator wants to compare the proportion of patients who recover within a week between two treatments. Which statistical method should be used?

Accepted Answer

Two-sample proportion confidence interval.

Question 8

Which of the following statements about hypothesis testing is correct?

Accepted Answer

The null hypothesis states there is no effect or difference.

Question 9

In a hypothesis test for a single proportion, which of the following is the correct null hypothesis?

Accepted Answer

$$H_0$$: p = $$p_0$$

Question 10

A researcher tests whether the proportion of smokers in two cities is the same. The p-value is 0.03. What is the correct interpretation at the 0.05 significance level?

Accepted Answer

There is sufficient evidence to reject the null hypothesis and conclude the proportions differ.

Question 11

Which of the following best describes a 'statistic' in the context of inferential statistics?

Accepted Answer

A value that describes a sample.

Question 12

If you are using StatCrunch to calculate a confidence interval for a proportion, which information do you need to input?

Accepted Answer

Sample size and number of successes.

Question 13

A pharmaceutical company wants to test if a new drug is more effective than the current standard. Which type of hypothesis test should they use?

Accepted Answer

Two-sample proportion hypothesis test.

Question 14

Which of the following is NOT a requirement for using the Central Limit Theorem for proportions?

Accepted Answer

The population must be normally distributed.

Question 15

A confidence interval for a proportion is calculated as $$0.25 \pm 0.05. $$What does this mean in context?

Accepted Answer

We are 95% confident the true proportion is between 0.20 and 0.30.

Question 16

Which of the following is a correct interpretation of a 99% confidence interval for a population proportion?

Accepted Answer

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

Question 17

Which of the following is the formula for the test statistic in a one-sample proportion hypothesis test?

Accepted Answer

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

Question 18

A school district wants to know if the proportion of students passing a standardized test is different from the state average of 80%. They sample 200 students and find 170 passed. What is the sample proportion?

Accepted Answer

$$\frac{170}{200} = 0.85$$

Question 19

Which of the following is a reason to use a two-sample proportion hypothesis test?

Accepted Answer

To compare the effectiveness of two different treatments.

Question 20

A researcher wants to test if the proportion of left-handed students in two universities is the same. Which is the correct null hypothesis?

Accepted Answer

$$H_0$$: $$p_1$$ = $$p_2$$

Statistics Exam 3 Study Guide: Sampling, Confidence Intervals, and Hypothesis Testing

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