Section 6.4-CI:Confidence Interval for a

Difference in Means

Example 1: The Effect of Tribulus

Tribulus is a food supplement that some athletes use to enhance performance.A study on the effects of this supplement randomly assigned 20 athletes to take the supplement for a 20-day period and compared various characteristics to 12 similar athletes who were not given Tribulus. On the AAMP (anaerobic alactic muscle power) measurement, the mean for the Tribulus group was 1305.6 with a standard deviation of 177.3 and the mean for the control group was 1255.9 with a standard deviation of 66.8. Find and interpret a 90% confidence interval for the difference in mean AAMP between athletes taking Tribulus and those not taking it.The conditions are met for using a t-distribution. Are we 90% sure that Tribulus has an effect?

Quick Self-Quiz:Diet Cola and Calcium

Does diet cola wash calcium out of our systems? A study to investigate this question randomly assigned 16 healthy women to drink 24 ounces of either diet cola or water. Their urine was collected for three hours after ingestion and calcium excretion was measured. For the 8 diet cola drinkers, mean amount of calcium excreted was 56.0 mg with a standard deviation of 4.93. For the 8 water drinkers, the mean was 49.1 mg with a standard deviation of 3.64.Neither distribution had any significant outliers or skewness. (Why is this important?) Find and interpret a 95% confidence interval for the difference in mean amount of calcium excreted between diet cola drinkers and water drinkers. Does diet cola appear to have an effect?

Section 6.4-HT:Hypothesis Test for a

Difference in Means

Example 1: Cognition Score and Alcohol

A recent study asked college students to indicate the level of alcohol use, and in this example, we compare the group of students who said they were light drinkers to the group of students who said they were heavy drinkers.Each student was also given several cognitive skills tests and assigned a cognition z-score based on the performance on these tests. The 83 students who said they were light drinkers had a mean cognition z-score of 0.1302 with a standard deviation of 0.75, while the 16 students who said they were heavy drinkers had a mean cognition z-score of -0.2338 with a standard deviation of 0.65. Test, using a 5% significance level, to see if there is evidence that heavy drinkers have a lower mean cognitive level than light drinkers. If the results are significant, can we conclude from this study that heavy drinking affects cognitive ability?

Quick Self-Quiz:Restaurant Tips and Credit Cards

We analyze the percent tip left on 157 bills from the First Crush bistro in Northern New York State.The mean percent tip left on the 106 bills paid in cash was 16.39 with a standard deviation of 5.05. The mean percent tip left on the 51 bills paid with a credit card was 17.10 with a standard deviation of 2.47. Test to see if there is a difference in the mean percent of the bill left as a tip between bills paid with a credit card and bills paid with cash.