you have 40 golfers who come to you for lessons and you are trying to determine

Question

you have 40 golfers who come to you for lessons and you are trying to determine if standardizing equipment for your students will improve their scores. You had each of the 40 players play 5 rounds of golf with their non-standardized equipment and each player only reported the average of their 5 rounds. The average of all the scores was 79 strokes. You gave them all the same set of clubs and the same brand golf balls and after some time to adjust to the new clubs, you had the same 40 players play 5 rounds of golf woth their standardized equipment and each player only reported the aberage of their 5 rounds. The average 76.5 and the standard deviation was 2.3 strokes. At the 1% statistical significance level, did standardizing equipment improve the players scores?

Step 1: What is the Null and Alternative Hypothesis?
Step 2: What is the statistical level of significance?   

Step 3: What is the test statistic?
Step 4: What is the decision criteria ?
Step 5: Based on the sample, what is your decision?
you have 40 golfers who come to you for lessons and you are trying to determine if standardizing equipment for your students will improve their scores. You had each of the 40 players play 5 rounds of golf with their non-standardized equipment and each player only reported the average of their 5 rounds. The average of all the scores was 79 strokes. You gave them all the same set of clubs and the same brand golf balls and after some time to adjust to the new clubs, you had the same 40 players play 5 rounds of golf woth their standardized equipment and each player only reported the aberage of their 5 rounds. The average 76.5 and the standard deviation was 2.3 strokes. At the 1% statistical significance level, did standardizing equipment improve the players scores?

Step 1: What is the Null and Alternative Hypothesis?
Step 2: What is the statistical level of significance?   

Step 3: What is the test statistic?
Step 4: What is the decision criteria ?
Step 5: Based on the sample, what is your decision?


Step 1: What is the Null and Alternative Hypothesis?
Step 2: What is the statistical level of significance?   

Step 3: What is the test statistic?
Step 4: What is the decision criteria ?
Step 5: Based on the sample, what is your decision?
Step 1: What is the Null and Alternative Hypothesis?
Step 2: What is the statistical level of significance?   

Step 3: What is the test statistic?
Step 4: What is the decision criteria ?
Step 5: Based on the sample, what is your decision?

Explanation / Answer

Given that,
population mean(u)=79
sample mean, x =76.5
standard deviation, s =2.3
number (n)=40
null, Ho: >79
alternate, H1: <79
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.426
since our test is left-tailed
reject Ho, if to < -2.426
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =76.5-79/(2.3/sqrt(40))
to =-6.875
| to | =6.875
critical value
the value of |t | with n-1 = 39 d.f is 2.426
we got |to| =6.875 & | t | =2.426
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -6.8745 ) = 0
hence value of p0.01 > 0,here we reject Ho
ANSWERS
---------------
null, Ho: >79
alternate, H1: <79
test statistic: -6.875
critical value: -2.426
decision: reject Ho
p-value: 0

we don't have evidence that standardizing equipment improve the players scores

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