The Charpy V-notch (CVN) technique measures impact energy and is often used to determine whether or not a material experiences a ductile-to-brittle transition with decreasing temperature. Ten measurements of impact energy (in $J$) on specimens of steel cut at $60^\circ C$ are as follows:
64.3, 64.9, 63.9, 62.5, 64.8, 64.1, 63.2, 65.2, 62.9, 66.3
a) Find a 95% CI for $\mu$, the mean impact energy for that kind of steel.
[ Number , Number ] (Enter your answer correct to 2 decimal places)
b) Determine the minimum number of specimens so that we are 95% confident of estimating mean impact energy $\mu$ to within 0.4 $J$ of its correct value. Use the sample standard deviation from the above data as an initial guess of the value for the true standard deviation.
Number (Enter your answer as an integer)
c) What assumptions did you make to construct this confidence interval?
We have a random sample of specimens.
Sample size is large enough.
Impact energy is normal.