A golfer in the past averaged 80 on a certain course Now he

A golfer in the past averaged 80 on a certain course. Now he buys a new set of golf clubs and in 4 rounds averages 78 with SD of 2. At level of significance = .01, has his game improved? Do a t-test.

Solution

Set Up Hypothesis
Null, A golfer game is improved H0: U>80
Alternate, H1: U<80
Test Statistic
Population Mean(U)=80
Sample X(Mean)=78
Standard Deviation(S.D)=2
Number (n)=4
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =78-80/(2/Sqrt(4))
to =-2
| to | =2
Critical Value
The Value of |t | with n-1 = 3 d.f is 4.541
We got |to| =2 & | t | =4.541
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -2 ) = 0.06966
Hence Value of P0.01 < 0.06966,Here We Do not Reject Ho

We have evidence to support the golfer is improved