What Went Wrong?
1)
Consider the following question:
Suppose that a golfer keeps track of
how far he hits the ball when he practices his long shots, and he has found
over time that his distances have an average of 180 yards and a standard
deviation of 20 yards. Suppose that he
starts using a new brand of golf ball and wants to see whether his average
distance seems to improve. He hits 64
shots with the new ball and calculates his average distance to be 190
yards. Does this provide strong evidence
that the mean of his driving distances is greater than 180 with the new
ball? Explain.
Identify
the flaw in each of the following responses:
a)
Yes, because 190 is larger than 180.
b)
No. (190-180)/20 = 0.5, so 190 is less
than one standard deviation above the mean of 180. This outcome of 190 would not be a surprising
result even if the mean driving distance with the new ball were still 180.
c)
We can’t tell. Because the driving
distance might have a skewed distribution, we cannot use the empirical rule or
perform any normal probability calculations.
So we can’t tell if a sample mean of 190 is a surprising result if the
population mean were still 180.