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 255 yards on average. Suppose a random sample of 166 golfers be chosen so that their mean driving distance is 259.5 yards, with a standard deviation of 44. Conduct a hypothesis test where H0:μ=255 and H1:μ>255 by computing the following: (a) test statistic (b) p-value p= (c) If this was a two-tailed test, then the p-value is

Guest Apr 4, 2020

#1**+1 **

CalTheGreat Apr 4, 2020

#3**+1 **

Here is a video on this.

https://www.youtube.com/watch?v=KLnGOL_AUgA

If you do not like this video there are plenty of others.

Melody Apr 4, 2020

#18**+2 **

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 255 yards on average. Suppose a random sample of 166 golfers be chosen so that their mean driving distance is 259.5 yards, with a standard deviation of 44. Conduct a hypothesis test where H0:μ=255 and H1:μ>255 by computing the following: (a) test statistic (b) p-value p= (c) If this was a two-tailed test, then the p-value is

\(\mu=255\\ n=166\\ \bar X=259.5\\ S=44\\ Test \;Stat \;is \;Z\\ Z=\frac{\bar X-\mu}{\left( \frac{S}{\sqrt n} \right)}\\ Z=\frac{259.5-255}{\left( \frac{44}{\sqrt {166}} \right)}\\ Z=1.318\\ \\~\\ H_0:\quad \mu=255\\ H_A:\quad \mu>2.55\\ \\~\\ P(Z>1.318) =P(Z<-1.38) \qquad \text{You can use either}\)

Maybe you have to use a given table.

I like this site.

http://davidmlane.com/hyperstat/z_table.html

**\(\boxed{\bf\text {It gives the P value as 0.0938}}\)**

I am reasonably sure that is all correct.

__Coding__

\mu=255\\

n=166\\

\bar X=259.5\\

S=44\\

Test \;Stat \;is \;Z\\

Z=\frac{\bar X-\mu}{\left( \frac{S}{\sqrt n} \right)}\\

Z=\frac{259.5-255}{\left( \frac{44}{\sqrt {166}} \right)}\\

Z=1.318\\

\\~\\

H_0:\quad \mu=255\\

H_A:\quad \mu>2.55\\

\\~\\

P(Z>1.318)

=P(Z<-1.38)

Melody Apr 4, 2020

#19**+1 **

If it is a 2 tail test I do not know what the answer is. I'd have to watch the next video I guess.

Melody Apr 4, 2020

#21**0 **

Why don't you just say what you want to say in plain English?

Better still if you believe you are knowledgable why don't you just answer the question yourself.

Why are you hiding behind anonymity?

People who make snide comments behind a curtain of anonymity usually have no idea of any relevant thing.

Melody
Apr 4, 2020