SOLUTION: A simple sample of heights of 6400 Englishmen has a mean of 67.85 inches an a standard deviation of 2.56 inches, while a simple sample of heights of 1600 Australians has a mean of

Question 1123237: A simple sample of heights of 6400 Englishmen has a mean of 67.85 inches an a standard deviation of 2.56 inches, while a simple sample of heights of 1600 Australians has a mean of 68.55 inches and a standard deviation of 2.52 inches. Do the data indicate that Australians are on the average taller than Englishmen? Use 5% level of significance.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
With large sample sizes, normality may be assumed if sample is random.
Ho: Australians are same height or smaller
Ha: Australians are taller.
alpha=0.05 P{reject Ho|Ho true}
1 way z-test
critical value is z>1.645
test (68.55-67.85)/sqrt (sigma1^2/n1+sigma^2/n2); sqrt (0.004993)=0.070
z=(0.7)/0.0707=9.91
reject Ho, highly significant
Australians on average are taller than Englishmen. Note: with samples this large, the power to detect a difference is very large. Note: z-test is appropriate with samples this large.

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