Question

Professional Golfers’ Earnings Two random samples of earnings of professional golfers were selected. One sample was taken from the Professional Golfers Association, and the other was taken from the Ladies Professional Golfers Association. At a=0.10, is there a difference in the means? The data are in thousands of dollars. Use the critical value method with tables.

PGA 1147, 1344, 9188, 5687, 10508, 4910, 8553, 7573, 375

LPGA. 48, 76, 863, 100, 1876, 2029, 4364

Assume the variables are normally distributed and the variances are unequal.

Part 2 of 5 Find the critical value(s). Round the answer(s) to at least three decimal places. If there is more than one critical value, separate them with commas. Critical value(s):

Answer 1

Solution:

The given data is as follows:

PGA	LPGA
1147	48
1344	76
9188	863
5687	100
10508	1876
4910	2029
8553	4364
7573
375

I have used excel to solve this problem.

Step 1: Let 1 be the sample mean for PGA and 2 be the sample mean for LPGA.

The hypothesis for the test are given as follows:

H0:1 =2

H1:1 2

The appropriate test is two-sample independent t-test.

Step 2:Let us follow these steps in excel to find the result.

• Enter the data with labels in excel.
• Go to data>data analysis
• Select t-test: two sample assuning equal variance
• Select rangs, PGA as variable 1 and LPGA as variable 2
• Enter Hypothesized mean difference as 0.
• Enter alpha=0.1
• Click OK

The output from the excel is as below:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	5476.11111	1336.571
Variance	14395506.1	2489767
Observations	9	7
Hypothesized Mean Difference	0
df	11
t Stat	2.96045522
P(T<=t) one-tail	0.00648237
t Critical one-tail	1.36343032
P(T<=t) two-tail	0.01296473
t Critical two-tail	1.79588482

From theabove table t-stat=2.96 which isgreater than t-critical=1.79. So we reject null hypothesis and conclude that there is difference im means.