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Owner: naweiss@sc
Created: Dec 18, 2010
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ES8 Report 10.2
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You can use StatCrunch to perform the pooled t-interval procedure. To illustrate, we discuss the StatCrunch solution to Example 10.4 of your text. 

      

Example   The Pooled t-Interval Procedure

 

Faculty Salaries    The American Association of University Professors (AAUP) conducts salary studies of college professors and publishes its findings in AAUP Annual Report on the Economic Status of the Profession. Independent simple random samples of 35 faculty members in private institutions and 30 faculty members in public institutions yielded the annual salaries, in thousands of dollars, displayed in Data set 1. Find a 95% confidence interval for the difference between the mean salaries of faculty in private and public institutions. Apply the pooled t-interval procedure. 

Data set 1. Samples of annual salaries for faculty   [Info]
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Solution   Let µ1 and µ2 denote the mean salaries of all faculty in private and public institutions, respectively. We want to find a 95% confidence interval for µ1µ2. Proceed as follows.

 

1       Choose Stat T statistics Two sample with data

2       Click the arrow button at the right of the Sample 1 in drop-down list box and select PRIVATE

3       Click the arrow button at the right of the Sample 2 in drop-down list box and select PUBLIC

4     Check the Pool variances check box

5     Click Next >

6     Select the Confidence Interval option button

7     Type 0.95 in the Level text box

8     Click Calculate


The output that you obtain should match that presented in Result 1. It shows that the required confidence interval is from 2.4873981 (L. Limit) to 27.541174 (U. Limit). We can be 95% confident that the difference between the mean salaries of faculty in private institutions and public institutions is somewhere between $2,487 and $27,541. In other words, we can be 95% confident that the mean salary of faculty in private institutions exceeds that of faculty in public institutions by somewhere between $2,487 and $27,541.


Result 1: Pooled t-interval on the salary data   [Info]
95% confidence interval results:
μ1 : mean of PRIVATE
μ2 : mean of PUBLIC
μ1 - μ2 : mean difference
(with pooled variances)
Difference Sample Mean Std. Err. DF L. Limit U. Limit
μ1 - μ2 15.014286 6.2686453 63 2.4873981 27.541174

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