Specifications for a small engine call for a mean air flow,μ, through the engine (at 5000 revolutions per minute) of more than 160 liters per minute. The engine maker’s engineers are investigating whether or not the day’s production of the engine meets this specification. A random sample of engines is selected and their air flows over one minute are measured, with these results (in liters per minute): 159.7, 161.9,164.7, 159.2, 161.3, 161.8, 162.9, 161, 158.5, 161.2. A normal probability plot looks reasonably straight. We will assume that these air flows are normally distributed.

a) Run a hypothesis test of H0:μ= 160 vs. HA: μ >160 at significance levelα= 0.05.

(b) What does the test say about whether the day’s engines meet this specification?

(c) Find an appropriate 95% confidence interval for μ.

(d) Can you directly compare the hypothesis test result and a two tailed confidence interval?