(TCO D) It seems like professional golfers are hitting their drives longer and l

Question

(TCO D) It seems like professional golfers are hitting their drives longer and longer each year. A random sample of 50 drives from 50 golfers yields the following.

Sample Size = 50 golfers
Sample Mean = 295 yd
Sample Standard Deviation = 16 yd

Does the sample data provide evidence to conclude that the mean drive length is over 290 yd (using a = .05)? Use the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.
b. State the level of significance.
c. Find the critical value (or values), and clearly show the rejection and nonrejection regions.
d. Compute the test statistic.
e. Decide whether you can reject Ho and accept Ha or not.
f. Explain and interpret your conclusion in part e. What does this mean?
g. Determine the observed p-value for the hypothesis test and interpret this value. What does this mean?
h. Does the sample data provide evidence to conclude that the mean drive length is over 290 yd (using a= .05)?

Explanation / Answer

a)H0: mean drive length=290

Ha: mean drive length> 290

b)level of significance=0.05

c) critical value=1.65

rejection region >1.65

d) testvalue=(295-290)/(16/sqrt50)=2.2097

e)as test value>1.65

we can reject h0 and accept Ha

f)this means the sample data provide sufficient evidence to conclude that the mean drive length is over 290 yd

g)p value=0.1355

this means smallest level of significance for which this is true is 0.01355

h)yes the sample data provide evidence to conclude that the mean drive length is over 290 yd

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