Question

Suppose that a travel bureau claims that the trees in a forest are 85 feet tall on average, with a standard deviation of 2 feet. If you took a sample of 64 trees, which of the following mean heights would be outside the 95% confidence interval?


A. 85.2 feet
B. 84.8 feet
C. 84.4 feet
D. 84.6 feet

Answer 1

the 95% confidence interval includes +- 2 std errors from the mean

std error for a sample size is:
\[\frac{s}{\sqrt{n}} = \frac{2}{\sqrt{64}} = \frac{1}{4}\]
95% confidence interval is
\[85 \pm 2(\frac{1}{4}) = (84.5 , 85.5)\]
only one of the answers is outside this interval