Question

1 point) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 260260 yards on average. Suppose a random sample of 106106 golfers be chosen so that their mean driving distance is 259.1259.1 yards. The population standard deviation is 48.248.2. Use a 5% significance level.

Calculate the followings for a hypothesis test where H0:μ=260H0:μ=260 and H1:μ<260H1:μ<260 :

   The test statistic is    
The final conclustion is

A. There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260
B. There is sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260

Answer 1

Solution :

= 260

=259.1

=48.2

n = 106

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 260

Ha :     260

Test statistic =z

= ( - ) / z / n

= (259.1-260) / 48.2 / 106

= -0.19

Test statistic = z = -0.19

P(z <  -0.19 ) =  0.4247

P-value = 2 *0.4247

= 0.05  

P-value >

8494 > 0.05

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the mean driving distance is equal to 260