In: Statistics and Probability
A club professional at a major golf course claims that the course is so tough that even professional golfers rarely break par of 73. The scores from a random sample of 20 professional golfers are listed below. Find the test statistic x to test the club professional's claim. 72 70 73 73 76 75 67 79 73 78 70 72 74 74 81 79 73 75 76 66
Answer choices: 6, 10, 4, 14
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: u < 73.0
Alternative hypothesis: u > 73.0
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n)
S.E = 0.8602
DF = n - 1
D.F = 19
t = (x - u) / SE
t = 0.93
where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of 0.93.
Thus the P-value in this analysis is 0.182.
Interpret results. Since the P-value (0.182) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that that even professional golfers rarely break par of 73.