Two manufacturers of preworkout drink formulas INTENSITY and

Two manufacturers of pre-workout drink formulas, INTENSITY and ULTIMATE FOCUS, have made conflicting claims regarding the effectiveness of their drinks. Tests were performed to evaluate each. The independent testing company tried INTENSITY on 100 athletes and found the mean effectiveness time was 85.0 minutes. A sample of 81 athletes tried ULTIMATE FOCUS and the mean effectiveness time was 86.2 minutes. Assume the population standard deviations given by the manufacturer are 6.0 minutes for INTENSITY and 6.8 minutes for ULTIMATE FOCUS. Does the evidence suggest a difference in the amount of effectiveness time? Use the 0.05 significance level and the five-step procedure.

Solution

Let mu1 be the mean for INTENSITY
Let mu2 be the mean for ULTIMATE FOCUS

The test hypothesis:

Ho: mu1=mu2 (i.e. null hypothesis)

Ha: mu1 not equal to mu2 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(85-86.2)/sqrt(6^2/100+6.8^2/81)

=-1.24

It is a two-tailed test.

Given a=0.05, the critical values are Z(0.025) =-1.96 or 1.96 (from standard normal table)

The rejectoin regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=-1.24 is between -1.96 and 1.96, we do not reject the null hypothesis.

So we can not conclude that the evidence suggest a difference in the amount of effectiveness time