Independent Samples: Confidence Intervals Lecture 40 Sections 11.4 – 11.5 Wed, Apr 11, 2007

Confidence Intervals Confidence intervals for 1 – 2 use the same theory. The point estimate isx1 –x2. The standard deviation ofx1 –x2 is or approximately

Confidence Intervals The confidence interval is or ( known, large samples) ( unknown, large samples) ( unknown, normal pops., any size samples)

Confidence Intervals The choice depends on Whether  is known. Whether the populations are normal. Whether the sample sizes are large.

Example Find a 95% confidence interval for 1 – 2 in Example 11.4, p. 699. x1 –x2 = 3.2. sp = 5.052. Use t = 2.101. The confidence interval is 3.2  (2.101)(2.259) = 3.2  4.75.

The TI-83 and Means of Independent Samples To find a confidence interval for the difference between means on the TI-83, Press STAT > TESTS. Choose either 2-SampZInt or 2-SampTInt. Choose Data or Stats. Provide the information that is called for. 2-SampTTest will ask whether to use a pooled estimate of . Answer “yes.”

Confidence Intervals for p1^ – p2^ The formula for a confidence interval for p1^ – p2^ is Caution: Note that we do not use the pooled estimate for p^. because we are not assuming that p1 = p2.

TI-83 – Confidence Intervals for p1^ – p2^ Press STAT > TESTS > 2-PropZInt… Enter x1, n1 x2, n2 The confidence level. Select Calculate and press ENTER.

TI-83 – Confidence Intervals for p1^ – p2^ In the window the following appear. The title. The confidence interval. p1^. p2^. n1. n2.

Example Find a 95% confidence interval using the data in the gender-gap example.