Confidence Intervals and Margin of Error Quiz

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2. True or False: The margin of error is inversely related to the square root of the sample size.

True

False

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4. True or False: Increasing the confidence level always decreases the width of the confidence interval.

True

False

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6. Which scenario would result in the smallest margin of error?

Large sample, 90% confidence level

Small sample, 99% confidence level

Large sample, 99% confidence level

Small sample, 90% confidence level

7. True or False: A 99% confidence interval is always more useful than a 95% confidence interval.

True

False

8. A researcher reports a 95% confidence interval of [50, 60] for average customer satisfaction. What is the point estimate?

50

55

60

5

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10. If you want to reduce the margin of error by half, by what factor should you increase the sample size?

2 times

4 times

10 times

0.5 times

11. A confidence interval is a range of values used to estimate a population parameter. What does the confidence level (e.g., 95%) represent?

The probability the true parameter lies within the interval

The percentage of data points in the sample

The margin of error multiplied by the sample size

The standard deviation of the sample

12. When should you use a t-distribution instead of a z-distribution for constructing confidence intervals?

When the sample size is very large

When the population standard deviation is unknown and sample is small

When the population is normally distributed

When the margin of error is small

13. The standard error is the standard deviation of the sampling distribution. How is it calculated for a sample mean?

Standard deviation divided by sample size

Standard deviation divided by the square root of sample size

Sample size divided by standard deviation

Standard deviation multiplied by sample size

14. Which of the following statements about confidence intervals is true?

A 99% CI is narrower than a 95% CI for the same data

A 99% CI is wider than a 95% CI for the same data

Confidence level does not affect interval width

A wider interval always indicates better accuracy

15. A poll reports that 60% of voters support a candidate with a margin of error of ±3%. What does this margin of error tell us?

The true population percentage is between 57% and 63%

3% of respondents were unsure

The sample size was exactly 1000

The confidence level is always 95%

16. For a normal distribution, a 95% confidence level corresponds to approximately how many standard deviations from the mean?

1 standard deviation

1.96 standard deviations

2.5 standard deviations

3 standard deviations

17. The margin of error formula includes the critical value (z* or t*), standard deviation, and sample size. How does increasing sample size affect the margin of error?

It increases proportionally

It decreases proportionally

It decreases by the square root of n

It remains constant

18. A researcher collects a sample of 100 students and calculates a 95% confidence interval for average study hours. If the sample mean is 12 hours and the margin of error is 2 hours, what is the confidence interval?

[10, 14]

[11, 13]

[12, 14]

[10, 12]

19. The margin of error in a confidence interval is directly proportional to the critical value. What happens to the margin of error if you decrease the confidence level from 99% to 95%?

It increases

It decreases

It stays the same

It doubles

20. Which factor increases the width of a confidence interval?

Larger sample size

Higher confidence level

Lower standard deviation

Smaller population size

Data+ V2 Confidence Intervals and Margin of Error Quiz

1. A confidence interval for a population mean is calculated as 45 ± 5. The margin of error is____.

2.

What first name or nickname would you like us to use?

2. True or False: The margin of error is inversely related to the square root of the sample size.

3. A survey of 400 customers shows 70% are satisfied, with a 95% confidence margin of error of ±4.5%. The confidence interval is approximately____.

4. True or False: Increasing the confidence level always decreases the width of the confidence interval.

5. The confidence interval formula is: point estimate ± (critical value × standard error). The term (critical value × standard error) equals the____.

6. Which scenario would result in the smallest margin of error?

7. True or False: A 99% confidence interval is always more useful than a 95% confidence interval.

8. A researcher reports a 95% confidence interval of [50, 60] for average customer satisfaction. What is the point estimate?

9. The critical value for a 90% confidence level using the normal distribution is approximately____.

10. If you want to reduce the margin of error by half, by what factor should you increase the sample size?

11. A confidence interval is a range of values used to estimate a population parameter. What does the confidence level (e.g., 95%) represent?

12. When should you use a t-distribution instead of a z-distribution for constructing confidence intervals?

13. The standard error is the standard deviation of the sampling distribution. How is it calculated for a sample mean?

14. Which of the following statements about confidence intervals is true?

15. A poll reports that 60% of voters support a candidate with a margin of error of ±3%. What does this margin of error tell us?

16. For a normal distribution, a 95% confidence level corresponds to approximately how many standard deviations from the mean?

17. The margin of error formula includes the critical value (z* or t*), standard deviation, and sample size. How does increasing sample size affect the margin of error?

18. A researcher collects a sample of 100 students and calculates a 95% confidence interval for average study hours. If the sample mean is 12 hours and the margin of error is 2 hours, what is the confidence interval?

19. The margin of error in a confidence interval is directly proportional to the critical value. What happens to the margin of error if you decrease the confidence level from 99% to 95%?

20. Which factor increases the width of a confidence interval?