Stat 211 Handout 9 (Chapter 9): Inferences Based on Two Samples tests

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Dependent Samples- Paired Data

Population characteristics: Difference between two population means, _D=₁-₂.

₀ is the claimed constant.

Assumption: the difference distribution should be normal.

Test statistics:

where D=X-Y and

and

are the corresponding sample average and the standard deviation of D. Both X and Y must have n observations.
Decision can be made in one of the two ways:
(a) Let t* be the computed test statistic values.

Lower tailed test	P-value = P(t
Upper tailed test	P-value = P(t>t*)
Two-tailed test	P-value = 2P(t > \|t\| )=2P(t <- \|t\| )

In each case, you can reject H₀ if P-value   and fail to reject H₀ (accept H₀) if P-value > 

(b) Rejection region for level  test:

Lower tailed test	t  -t__;n-1
Upper tailed test	t  t__;n-1
Two- tailed test	t  -t__/2;n-1 or t  t__/2;n-1

100(1-)% confidence Intervals with the same assumptions,

Example 10: The manager of a fleet of automobiles is testing two brands of radial tires. He assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The descriptive statistics for the data are shown below (in kilometers). Find the 99% confidence interval on the difference in mean life. Which brand would you prefer based on this calculation? Is there an alternative method to answer this question instead of computing the confidence interval?
Variable N Mean Median StDev SE Mean Minimum Maximum Q1 Q3

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