Question

An article investigated the consumption of caffeine among women. A sample of 40 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 240.944 mg with a standard deviation of 207.976 mg.

In the article, researchers would like to include a 99% confidence interval. The values below are t critical point corresponding to 90%, 95%, 98%, and 99% confidence. Which critical point corresponds to 99% confidence?

a) 1.685

b) 2.426

c) 2.708

d) 2.023

With 99% 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.) If the level of confidence were changed to 98%, what effect would this have on the width of the calculated confidence interval?

a) the interval would narrow

b) the interval would widen

c) there would be no effect on the interval

Answer 1

Df = 40 - 1 = 39

At 99% confidence interval the critical value is t^* = 2.708

Option - c is correct.

The 99% confidence interval is

+/- t^* * s/

= 240.944 +/- 2.708 * 207.976/

= 240.944 +/- 89.0496

= 151.8944, 329.9936

Option - a) the interval would narrow.

Because if the confidence level decreases, the margin of error also decreases, so that the confidence interval becomes narrower.