Question

Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball quite far. Designers, therefore, have proposed that new golf courses need to be built expecting that a typical player can hit the golf ball more than 225 m on average.

Suppose historical data show that the driving distances of typical golfers have a standard deviation of 42. A random sample of 36 golfers were chosen and their mean driving distance is 239 m. Test a suitable hypothesis to examine whether the data support the designers' concern at α = 0.1?

Answer 1

Given:

= 225 m, n = 36, = 239 m, = 42, = 0.1

Hypothesis:

Ho: = 225 m

Ha: > 225 m

Test statistic:

Critical value:

Z =Z_0.1 = 1.28

Decision Rule:

Z > Z, Then Reject Ho at % level of significance.

Conclusion:

Since the observed value of the test statistic Z = 2, is Larger than the critical value 1.28 at 10% level of significance.

So, Reject Ho at 10% Level of significance.

Therefore, typical player can hit the golf ball more than 225 m on average.