A study based on a sample of size 81 reported a mean of 86 with a margin of error of 11 for 95%...

Question:

A study based on a sample of size {eq}81 {/eq} reported a mean of {eq}86 {/eq} with a margin of error of {eq}11 {/eq} for {eq}95\% {/eq} confidence.

(a) Give the {eq}95\% {/eq} confidence interval.

(b) If you wanted {eq}99\% {/eq} confidence for the same study, would your margin of error be greater than, equal to, or less than 11? Explain your answer.

1) The new margin of error would be less than 11. A smaller margin of error is needed to be more confident that the interval includes the true mean.

2) It is impossible to determine if the margin of error will change using the information given.

3) The new margin of error would be equal to 11. The margin of error will not change when the confidence level is increased.

4) The new margin of error would be greater than 11. A wider margin of error is needed to be more confident that the interval includes the true mean.

5) The confidence level should never be changed for the same study.

Confidence Interval:

Confidence interval gives range between two values population parameter is most likely to be contained. The length of the interval depends on sample size, level of confidence and sample variability.

Answer and Explanation:

a).

The confidence interval occurs plus and minus margin of error from the point estimate (sample mean):

{eq}(\bar X\pm E)\\(86\pm 11)\\(75, 97) {/eq}


b).

The correct answer is: 4) The new margin of error would be greater than 11. A wider margin of error is needed to be more confident that the interval includes the true mean

99% confidence interval will be wider than 95% confidence interval. This is because increase in confidence level increases critical value which increases margin of error.


Learn more about this topic:

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Finding Confidence Intervals with the Normal Distribution

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 3
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