A writer for Autos R Us magazine believes new cars are less expensive in the Col

Question

A writer for Autos R Us magazine believes new cars are less expensive in the Columbus area than they are in the Denver area. To test her theory, she selects the most popular make, model, and trim of car and randomly samples 46 such sales in the Columbus area which results in a sample mean price of $24,650 with a standard deviation of $1050. She also randomly samples 42 such sales in the Denver area and obtains a sample mean price of $25,785 with a sample standard deviation of $1100. At the .05 level of significance, is there enough evidence to conclude that the mean price of new cars is lower in the Columbus area than in the Denver area? Assume the price of new cars is normally distributed. List and clearly label all eight steps.

Explanation / Answer

Let 1 be the mean if cars in the Columbus area and 2 be the mean if cars in the Denver area.

H0: 1 = 2
Ha: 1 < 2

Significance level, = 0.05

One tailed two sample t test.

Standard error, SE = sqrt[ (s12/n1) + (s22/n2) ] = sqrt[10502/46 + 11002/42] = 229.7322683

Degrees of freedom, DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] } = 84.3835 = 84

Test statistic, t = [ (x1 - x2) - 0 ] / SE = (24650 - 25785)/229.7322683 = -4.9405

p-value = 0.00000196 < 0.05, Reject H0, There is sufficient evidence to suggest that the mean price of new cars in Columbia area is lower than the Denver area.

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