Q: Given a sample proportion $$\hat{p} = 0.6$$ from a sample of $$n = 150$$, what is the standard error of $$\hat{p}$$?

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

Q: A sample of 80 watermelon prices yields a mean of $$6.88 and a standard deviation of 1.92. $$What is the 90% confidence interval for the mean price per 100 pounds?

$$6.88 \pm 1.645 \times \frac{1.92}{\sqrt{80}}$$

Question 1

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

Accepted Answer

If we took many samples and built a confidence interval from each, about 95% of those intervals would contain the true population proportion.

Question 2

A researcher wants to estimate the proportion of defective products in a large shipment. She samples 200 items and finds 16 are defective. What is the point estimate for the population proportion?

Accepted Answer

$$\frac{16}{200} = 0.08$$

Question 3

Which of the following is NOT an assumption or condition that must be checked before constructing a confidence interval for a population proportion?

Accepted Answer

The population must be normally distributed

Question 4

Given a sample proportion $$\hat{p} = 0.6$$ from a sample of $$n = 150$$, what is the standard error of $$\hat{p}$$?

Accepted Answer

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

Question 5

A 99% confidence interval for a population proportion is calculated as $$\hat{p} \pm 2.576 	imes SE(\hat{p}). $$What does the value 2.576 represent?

Accepted Answer

The critical value $$z_{\alpha/2}$$ for a 99% confidence level

Question 6

If a 95% confidence interval for a population proportion is [0.12, 0.18], what is the margin of error?

Accepted Answer

$$0.03$$

Question 7

Which of the following will decrease the width of a confidence interval for a population mean, assuming all other factors remain constant?

Accepted Answer

Increasing the sample size

Question 8

A candidate wants to estimate voter support within 2 percentage points with 95% confidence. No prior estimate is available. What value of $$\hat{p}$$ should be used to determine the required sample size?

Accepted Answer

$$0.5$$

Question 9

Suppose a 95% confidence interval for the mean IQ score is [87.55, 101.57]. Which of the following is a correct interpretation?

Accepted Answer

We are 95% confident that the true mean IQ score is between 87.55 and 101.57.

Question 10

Which formula is used to calculate the required sample size $$n to $$estimate a population mean with margin of error $$ME$$ and confidence level $$1-\alpha ($$assuming population standard deviation $$\sigma is $$known)?

Accepted Answer

$$n = \left( \frac{z_{\alpha/2} \sigma}{ME} \$$right)^2$$

Question 11

A food producer samples 100 bags of potatoes and finds a 95% confidence interval for the proportion of defective bags is [0.005, 0.008]. The supplier guarantees no more than 1% defective. What should the producer do?

Accepted Answer

Accept the lot because the entire interval is below 1%.

Question 12

If the sample size is increased while keeping the confidence level constant, what happens to the margin of error?

Accepted Answer

It decreases

Question 13

Which of the following is the correct formula for a 95% confidence interval for a population mean when the population standard deviation is unknown and $$n \geq 60$$?

Accepted Answer

$$\bar{y} \pm 1.96 \frac{s}{\sqrt{n}}$$

Question 14

A sample of 80 watermelon prices yields a mean of $$6.88 and a standard deviation of 1.92. $$What is the 90% confidence interval for the mean price per 100 pounds?

Accepted Answer

$$6.88 \pm 1.645 	imes \frac{1.92}{\sqrt{80}}$$

Question 15

Which of the following statements about the relationship between confidence level and precision is correct?

Accepted Answer

Increasing the confidence level decreases the precision of the interval.

Question 16

If the Success/Failure Condition is not met for a confidence interval for a proportion, what adjustment can be made?

Accepted Answer

Add two successes and two failures to the sample and recalculate the interval.

Question 17

Which of the following is a property of an unbiased estimator?

Accepted Answer

Its expected value equals the parameter being estimated.

Question 18

A 90% confidence interval for a population proportion uses which critical value?

Accepted Answer

$$z_{\alpha/2} = 1.645$$

Question 19

Which of the following is NOT a correct way to reduce the margin of error in a confidence interval for a mean?

Accepted Answer

Increase the population standard deviation

Confidence Intervals for Proportions and Means

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