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 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 235 yards on average. Suppose a random sample of 192 golfers was collected and their sample mean driving distance was 233.8 yards. The population standard deviation is 46.6. Use a 5% significance level.
Conduct a hypothesis test where H_0: \mu = 235 and H_1:\mu > 235 by computing the following:
(a) \ test statistic ______________\
(b) \ p-value p = ______________

Answer 1

Answer:

test statistic is ≈ -0.36

p-value is  ≈ 0.64

There is no significant evidence that the average golfer can hit the ball more than 235 yards on average.

Step-by-step explanation:

a hypothesis test where H_0: mu = 235 and H_1:mu > 235

test statistic can be calculated as follows:

z=$\frac{X-M}{\frac{s}{\sqrt{N} } }$ where

• sample mean driving distance (233.8 yards)

• M is the average expected distance that the average golfer can hit the ball under null hypothesis. (235 yards)

• s is the standard deviation (46.6 yards)

• N is the sample size (192)

Then test statistic is z=$\frac{233.8-235}{\frac{46.6}{\sqrt{192} } }$ =-0.3568

p-value is  0.64 >0.05

There is no significant evidence that the average golfer can hit the ball more than 235 yards on average.