Confidence intervals!

Question

An article investigated the consumption of caffeine among women. A sample of 58 women were asked to monitor their caffeine intake over the course of one day. The mean amount of caffeine consumed in the sample of women was 204.346 mg with a standard deviation of 212.321 mg. In the article, researchers would like to include a 95% confidence interval.   

1. The values below are t critical point corresponding to 90%, 95%, 98%, and 99% confidence. Which critical point corresponds to 95% confidence? 
2. 1.672
3. 2.665
4. 2.394
5. 2.002
6. With 95% confidence, we estimate the mean amount of caffeine consumed by women is between  mg and  mg. (Round the limits of your interval to 4 decimal places.)
7. If the level of confidence were changed to 98%, what effect would this have on the width of the calculated confidence interval?
8. the interval would narrow
9. the interval would widen
10. there would be no effect on the interval

Answer 1

The bigger the confidence level, the wider the confidence interval and thus the larger the critical value of t.

Since 95% is the 3rd shortest CI, it will have the 3rd largest t or 2.002.

CI = 204.346 +/- 2.002 * 212.321/sqrt(58)

leave it to you to make the final computations.

If the confidence level was increased to 98, the CI would widen, as the critical t would increase, with all other values being held constant.