Question 1187957: A monograph written in 1902 states that the mean height of adult American males is 67.0 inches with a standard deviation of 3.5 inches. Wishing to see if these values have changed over the twentieth century the geneticist measured a random sample of 28 adult American males and found that X = 69.4 inches and s = 4.0 inches. Are these values significantly different from the values published in 1902
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! this is a 1 sample t-test
Can do this as a confidence interval assuming that the sd of the sample is an unbiased estimator of that of the population. The CI of a sample of 28 in this example would contain 3.5, that of the population, so a 1-sample t-test and t-interval could be done.
t-test
Ho; mean is 67.0
Ha: mean is not 67.0
alpha=0.05 p{reject Ho|Ho true}
test is a t 0.975 df=27
critical value is |t| > 2.052
t=(69.4-67)/4/sqrt(28)
=3.17
reject Ho, the height is more
p-value=0.0037
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half-interval is mean +/- t(0.975, df=27)s/sqrt(n) for a 95% interval]
=2.052*4.0/sqrt(28)
=1.55
the 95% t-interval is (67.85, 70.95)
Since 67.0 is not in the interval, there values are significantly different.
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