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 230 yards on average. A random sample of 177 golfers show that their mean driving distance is 230.7 yards, with a standard deviation of 41.8.

1. Set up the null and alternative hypotheses to test for the designers belief.
a. H0 : µ ≥ 230 versus Ha : µ < 230
b. H0 : µ = 230.7 versus Ha : µ ≠ 230.7
c. H0 : µ ≥ 230.7 versus Ha : µ < 230.7
d. H0 : µ ≤ 230.7 versus Ha : µ > 230.7
e. H0 : µ ≤ 230 versus Ha : µ > 230
2. Find the value of the standardized test statistic.
a. 0.125
b. -0.125
c. 0.223
d. -0.7
e. 0.7
3. Find the P-value for the above mentioned test.
a. 0.8237
b. 0.0228
c. 0.5871
d. 0.4118
e. 0.0871

Answer 1

a) e) H0 : µ ≤ 230 versus Ha : µ > 230

b)
`t=(230.7-230)/((41.8)/(√(177)))=0.223`

c. 0.223

c)
`p_v =P(t_((176))>0.223)=0.4118`

d. 0.4118

Explanation:

Information given

`\bar X=230.7` represent the sample mean

`s=41.8` represent the sample standard deviation

`n=177` sample size

`\mu_o =230` represent the value to verify

t would represent the statistic

`p_v` represent the p value

Part a

We want to verify if the true mean is higher than 230 yards, the system of hypothesis would be:

Null hypothesis:
`\mu \leq 230`

Alternative hypothesis:
`\mu > 230`

The best option would be:

H0 : µ ≤ 230 versus Ha : µ > 230

Part b

The statistic is given by:

`t=(\bar X-\mu_o)/((s)/(√(n)))` (1)

Replacing the info given we got:

`t=(230.7-230)/((41.8)/(√(177)))=0.223`

Part c

The degrees of freedom are:

`df=n-1=177-1=176`

The p value would be given by:

`p_v =P(t_((176))>0.223)=0.4118`

d. 0.4118