Chapter 10 Statistical Inference for Two Samples Twice as much fun as one sample

10-2 Inference for a Difference in Means of Two Normal Distributions, Variances Known Two populations – count them, 1,..2

More on Two Normals Assumptions

Oh yes, the test statistic

Example 10-1

Type II Error and Choice of Sample Size Two-sided alternative: One-sided alternative: Now go to the Operating Characteristic Curves (VIIa-d)

Sample Size Formulas

Example 10-3

Confidence Interval on a Difference in Means, Variances Known

CI Example 10-4

Other Useful Formulae Upper Confidence Bound Lower Confidence Bound Choice of Sample Size

Hypotheses Tests for a Difference in Means, Variances Unknown Case 1:

The Two-Sample or Pooled t-Test

Example 10-5 We must do a difference of means test on this data.

Example 10-5

Minitab Output for Example 10-5

Type II Error and Choice of Sample Size

Chart VII(e) d =.74  =.15 d =.74  =.15

Hypotheses Tests for a Difference in Means, Variances Unknown Case 2: is distributed approximately as t with degrees of freedom given by

Example 10-6

The Data in a Normal Prob Plot

Example 10-6 (steps 1-5)

Example 10-6 (steps 6- 8)

Mean of Two Normal Distributions – Variance Unknown – Confidence Intervals Case 1:

Mean of Two Normal Distributions – Variance Unknown – Confidence Intervals Case 2:

The Next Example Louie Lush has collected the following data concerning the number of ounces of beer consumed per week by the typical UD student and the typical Wright-State student. Assuming the population variances are equal construct a 90% confidence interval for the difference in mean beer consumption between the two schools. Data: Ounces per student per week Wright State Univ of Dayton Sample mean Sample Variance Sample size1012 Pooled Variance:

More Next Example Wright State Univ of Dayton Sample mean Sample Variance Sample size1012 Unequal Variances: If you are interested in establishing a tavern near one of the two campus which one would you choose?

On to Excel…then Minitab These 2-sample tests are great but what can Excel do for me? To the Ever Excellent Excel Examples

Happiness is working a stat problem. Next Class I always work all the problems in the book.