Question

An article investigated the consumption of caffeine among women. A sample of 43 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 243.872 mg with a standard deviation of 209.05 mg. In the article, researchers would like to include a 90% confidence interval.   

• The values below are t critical point corresponding to 90%, 95%, 98%, and 99% confidence. Which critical point corresponds to 90% confidence?
  • 1.682
  • 2.698
  • 2.418
  • 2.018
• With 90% 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 99%, what effect would this have on the width of the calculated confidence interval?
  • the interval would narrow
  • the interval would widen
  • there would be no effect on the interval

Answer 1

Here we have to compute confidance interval for mean,

we know that,

#from t table

Therefore option 1 is correct.

critical point corresponds to 90% confidence is 1.682.

Here we compute 90% confidence interval for mean,

Given:

With 90% confidence, we estimate the mean amount of caffeine consumed by women is between 190.2501 mg and 297.4939 mg

Now,

we have to compute 99% confidance interval,

With 90% confidence, we estimate the mean amount of caffeine consumed by women is between 157.8602 mg and 329.8838 mg

If the level of confidence were changed to 99%, what effect would this have on the width of the calculated confidence interval is wider.

correct option is,

• the interval would widen