Question: Wall-Blues claims that its store brand of cough lozenge delivers soothing relief that lasts as long as the leading brand, Robinson’s. A sample of 72 Wall-Blues cough lozenges were tested and found to provide relief for 6.2 hours with a standard deviation s = 0.54 hours. A sample of 78 Robinson’s cough lozenges were also tested and found to provide relief for 5.9 hours with a standard deviation of s = 0.86 hours. We cannot assume that the population standard deviations are equal. At the .05 significance level, is there a difference in the number of hours of relief the two brands of cough lozenge provide?

Ha: \({{H}_{0}}:{{\mu }_{1}}={{\mu }_{2}}\)

H1:

= 0.05

Distribution: t-distribution

Test Statistic t = 2.579

P-value: p = 0.011

Decision on H0: Reject Ho

Interpretation: We have enough evidence to support the claim that there is a difference in the number of hours of relief the two brands of cough lozenge provide.