A club professional at a major
A club professional at a major golf course claims that thecourse is so tough that even professional golfers rarely break parof 73. The scores from a random sample of 20 professional golfersare listed below. Find the test statistic x to test the clubprofessional’s claim. 72 70 73 73 76 75 67 79 73 78 70 72 74 74 8179 73 75 76 66
Answer choices: 6, 10, 4, 14
Answer:
Solution:-
State the hypotheses. The first step is tostate the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 73.0Alternative hypothesis: u > 73.0
Note that these hypotheses constitute a one-tailed test. Thenull hypothesis will be rejected if the sample mean is toosmall.
Formulate an analysis plan. For this analysis,the significance level is 0.05. The test method is a one-samplet-test.
Analyze sample data. Using sample data, wecompute the standard error (SE), degrees of freedom (DF), and the tstatistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.8602DF = n – 1
D.F = 19t = (x – u) / SE
t = 0.93
where s is the standard deviation of the sample, x is the samplemean, u is the hypothesized population mean, and n is the samplesize.
The observed sample mean produced a t statistic test statisticof 0.93.
Thus the P-value in this analysis is 0.182.
Interpret results. Since the P-value (0.182) isgreater than the significance level (0.05), we cannot reject thenull hypothesis.
From the above test we have sufficient evidence in thefavor of the claim that that even professional golfers rarely breakpar of 73.
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