Question

Do professional golfers play better in the first round? Let row Y represent the score in the final round and row Z represent the score in the first round of the professional golf tournament. A random sample of the finalist gave the following data.

Y: Last     73 68 73 71 71     72 68 68 74

Z: First    66 70 64 71 65     71 71 71 71

Let a= score in the last round - score in the first round and sigma a = mean in the last round - mean in the first round. The population of paired difference of golf score has normal distribution with unknown standard deviation. At 10% level of significance, test the claim that professional golfers do better the first round.

Answer 1

To test, whether the professional golfers did better in the second round,

Let denote the population mean score of the golfers in the first round,
Let denote the population mean score of the golfers in the 2nd round,

Let

ie. to test,

The test statistic is calculated as:

- where is the mean difference, s² is the sample variance, n is the sample size.

Now, under the null hypothesis, the t statistic follows a t distribution with n-1 degrees of freedom.

Under the light of the given data,
We have the value of test statistic as 1.33 which follows a t distribution with 8 degrees of freedom

the p-value of the test statistic based on the given alternate hypothesis is obtained as 0.8904

Thus on light of the given data, we do not have enough information to reject the null hypothesis.