Researchers are testing the effectiveness of two pain relief medicines for headaches. A random sample of 50 individuals was randomly divided into two groups.One group used medicine #1 for a three month period and another group used medicine #2 for a three month period. Each group kept track of the time required to receive pain relief. Statistics on time to receive pain relief are provided in the table below.
Individuals using Medicine #1
Sample Size: n1=25
Sample Mean: x-bar1=22.5 minutes
Sample Standard Deviation: s1=3.5 minutes
Individuals using Medicine #2
Sample Size: n2=25
Sample Mean: x-bar2=24.6 minutes
Sample Standard Deviation: s2=3.8 minutes
At the 2% level of significance, can it be concluded that the mean time to receive pain relief is different for the two medicines? Assume the times to relief pain relief from each brands are normally distributed and the standard deviations of the two populations are equal.
Formulate and test the appropriate hypotheses. Use the critical value approach. Show work.