Serious golfers and golf equipment companies sometimes make use of golf equipment testing labs sometimes make use of golf equipment testing labs to obtain precise information about particular club heads, club shafts, and golf balls. One golfer requested information about the Jazz Fat Cat 5-iron from Golf Laboratories, Inc.
The company tested the club by using a robot to hit a Titleist NXT Tour ball six times with a head velocity of 85 miles per hour. The golfer wanted a club that, on average, would hit the ball more than 180 yards at that club speed.
The sample mean of the six strikes was 182.7 yards and the sample standard deviation was 2.7 yards.
Using the p-value approach, decide whether the data provides sufficient evidence to conclude that the club does what the golfer wants. Assume a 5% significance level.
I think the answer is something like this. Please correct me if I am wrong.
Null hypothesis: mu <= 180
Alt hypothesis: mu > 180
alpha = 0.05
x-bar = 182.7
s = 2.7
n = 6
degrees of freedom = 5
t = (182.7-180)/(2.7/sqrt(6)) = 2.449
On my t-table:
t_0.025 @ 5dof = 2.571
t_0.05 @ 5dof = 2.015
Since my t-value is between t_0.025 and t_0.05 I reject the null hypothesis. Is this correct?