Question

Consider the following example in which a paired comparison hypothesis test was conducted to determine if the average daily temperatures at the Montreal PET airport were more than 0.5 degrees colder (at a 2% significance level) than the corresponding temperatures at the Ottawa airport. The data set consisted of 12 pairs (TM - TO) with d = - 0.78 oC and sd = 1.03 oC. Where, TM: Average daily temperature at the Montreal airport TO: Average daily temperature at the Ottawa airport Someone solved the problem as below. But their solution includes some mistakes/omissions. You are asked to review their solution. You should find the mistakes/omissions and fix them. We can assume that the paired comparison is the correct approach here. Since you cannot return the question, you won’t be able to cross the mistakes on the solution and fix it right there. One option is for you to repeat the solution (as is) on your answer sheet and then fix the mistakes and fix them right there (with a different color pen). The other option is that you just write a list of the mistakes (with bullet points or numbers) and then in front of each mistake write the corrected form of it.

Hypotheses HO: d = –0.5, HA: d > –0.5

Calculated Statistic 4.305 1.03 12 0.78 0.5  − − − t calc =

Critical Statistic tcrit = –t0.01,12 = –2.718

Decision tcalc < -tcrit, so reject HO

Conclusion The daily maximum temperature at the Montreal PET airport is significantly more than 0.5 degrees colder than the average daily temperature at the Ottawa airport.

Answer 1

Hypotheses HO: d = –0.5, HA: d > –0.5

Standard error of mean difference, se = sd / = 1.03 / = 0.2973354

Calculated Statistic t calc = (Observed difference - Hypothesized difference) / se

= (-0.78 + 0.5)/0.2973354 = -0.9416975

Degree of freedom = n-1 = 12 - 1 = 11

Critical Statistic tcrit = = -2.718 (The degree of freedom is 11 and not 12)

Decision tcalc > -tcrit, so fail to reject HO

Conclusion The daily maximum temperature at the Montreal PET airport is not significantly more than 0.5 degrees colder than the average daily temperature at the Ottawa airport.