Question

Rendezvous Golf Course reports an average score of 73.2 strokes per game on the pro tour with a standard deviation of 2.8. Recently they made some design changes to some holes on the course and they are curious if the course average has changed. Using a 1% level of significance conduct a hypothesis test if a sample of 50 rounds of golf had a mean score of 72.1 strokes.

try to handwrite full solutions

Answer 1

H0: = 73.2

Ha: 73.2

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 72.1 - 73.2 ) / ( 2.8 / √( 50 ))
Z = -2.78

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.01 /2 ) = 2.576
| Z | > Z( α/2 ) = 2.78 > 2.576

Result :- Reject null hypothesis

We have sufficient evidence to support the claim that the course average has changed,