Question 1187957
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
-
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.