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 71 Wall-Blues cough lozenges were tested and found to provide relief for 5.2 hours with a standard deviation s = 0.44 hours. A sample of 77 Robinson’s cough lozenges were also tested and found to provide relief for 5.8 hours with a standard deviation of s = 0.76 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?

H0: \({{\mu }_{1}}={{\mu }_{2}}\)

H1: \({{\mu }_{1}}\ne {{\mu }_{2}}\)

\(\alpha \) = 0. 05

Test Statistic -5.9327

P-value: 0.0000

Decision on H0: Reject Ho

Interpretation: W e 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.

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