Question 1

A 95% confidence interval for the average time students spend studying per week is (12.4, 18.6). What is the sample mean?

Accepted Answer

$$15.5$$

Question 2

Given the confidence interval (5.2, 7.8) for average daily screen time (in hours), what is the margin of error?

Accepted Answer

$$1.3$$

Question 3

If the sample size $$n$$ increases while all other factors remain constant, what happens to the margin of error in a confidence interval?

Accepted Answer

The margin of error decreases because $$\sqrt{n} is in $$the denominator of the formula.

Question 4

How does increasing the confidence level from 90% to 99% affect the margin of error?

Accepted Answer

The margin of error increases because a higher confidence level requires a wider interval.

Question 5

Two studies estimate the same population mean. Study A has a narrow confidence interval, and Study B has a wide confidence interval. Which study provides a more precise estimate and why?

Accepted Answer

Study A, because a narrow confidence interval indicates greater precision.

Question 6

Suppose a 95% confidence interval for the mean systolic blood pressure in a population is (120, 140). What is the margin of error?

Accepted Answer

$$10$$

Question 7

A researcher wants to decrease the margin of error in a confidence interval for the mean. Which of the following strategies will achieve this?

Accepted Answer

Increase the sample size.

Question 8

The formula for the margin of error in a confidence interval for the mean is:

Accepted Answer

$$z^* \frac{\sigma}{\sqrt{n}}$$

Question 9

A 99% confidence interval for the mean commute time is (30, 50) minutes. What is the sample mean?

Accepted Answer

$$40$$

Question 10

If a confidence interval for the mean is (8, 12), which of the following is the correct calculation for the margin of error?

Accepted Answer

$$\frac{12 - 8}{2} = 2$$

Question 11

A study reports a 95% confidence interval for the mean cholesterol level as (180, 220) mg/dL. If the sample mean is recalculated as the midpoint, what is its value?

Accepted Answer

$$200$$

Question 12

Which of the following best describes the effect of a wider confidence interval?

Accepted Answer

It indicates less precision in estimating the population parameter.

Question 13

A 90% confidence interval for the mean weight of apples is (150g, 170g). What is the margin of error?

Accepted Answer

$$10g$$

Question 14

If the margin of error for a 95% confidence interval is $$3$$ and the sample mean is $$50$$, what is the confidence interval?

Accepted Answer

$$(47, 53)$$

Question 15

A hospital administrator wants to estimate the average length of stay for patients. She increases the sample size from 25 to 100. What is the effect on the margin of error, assuming all else is constant?

Accepted Answer

The margin of error is halved.

Question 16

Which of the following statements about confidence intervals is correct?

Accepted Answer

A narrower confidence interval means a more precise estimate of the population mean.

Question 17

A 95% confidence interval for the mean number of hours slept per night is (6.5, 8.5). What is the sample mean?

Accepted Answer

$$7.5$$

Question 18

If the confidence level is increased from 95% to 99%, what happens to the width of the confidence interval, assuming all else is constant?

Accepted Answer

The interval becomes wider.

Question 19

A researcher calculates a 95% confidence interval for the mean as (22, 28). What is the correct formula to find the sample mean?

Accepted Answer

$$\frac{22 + 28}{2}$$

Question 20

A 95% confidence interval for the mean test score is (70, 90). What is the margin of error?

Accepted Answer

$$10$$

Confidence Intervals & Margin of Error — Step-by-Step Guidance

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