Chapter11_2 - \ > - - -11 Inference for Distributions...

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\ ------ -- >- - - a p t e 11 Inference for Distributions 11.2 COMPARING TWQ MEANS Comparing two populations or two treatments is one of the most common sit- uations encountered in statistical practice. We call such situations two-sample problems. TWO-SAMPLE PROBLEMS I> 1, . The goal of inference is to compare the responses to two treatments or to compare the characteristics aftwo popuIations. We have a s'qprate sample from each .treatment or each population. . *; ' Two-sample problems Atwo-sample problem can arise fiom a randomized comparative experiment that randomly divides subjects into two groups and exposes each group to a different treatment Comparing random samples separately selected fiom two populations is also a ix+o--sample problem. Unlike the matched pairs designs studied earlier, there is no matching ofthe units in the two samples and the hxro samples can be of different sizes. Merence procedures for twccsample data differ fran'those for matched pairs. Here are some typical two.mple problems. EXAMPLE 11.9 m.0-$AMPLE PROBLEMS (a) A medical researcher is interested in the effect on blood pressure of added cal- cium in our diet. She conducts a randomized comparative eeeriment in which one group of subjects.receives a calcium supplement and a control group gets a placebo.
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11.1 Inference for the Mean of a ~oGlatio--~ TECHNOLOGY TOOLBOX t procedures on the TI-83/89 (continued) 1 - Select "Calculate" and press =-5.714285714 Sx=10.56429816 The results tell us that the 95% confidence interval for the true mean population difference in heal- ing rate is between -11.81 and 0.385 micrometers per hour. If the researchers wanted to keep the 95% confidence level but wanted a shorter, more precise confidence interval, they would need to use more newts in the experiment (that is, increase the sample size n). To perform tests of significance, recall that the null hypothesis in Exercise 11.20 (b) was "no change in healing rate" for the newts, while the alternative hypothesis said "changing the electric field lowers the healing rate." In symbols, Ho: E*.EXP-CO~OL = PDIFF = 0 Ha: E*.EXF-CO~TROL = E*.DlFF < O With the data stored in Ll/listl, go to STATRESTS (Tests menu on the TI-89). Choose 2: T-Test. Adjust your settings as shown. I T-Tes t 1npt:m Stats List: Li Freq : 1 P:wom 'PO -, - If you select "Calculate," the following screen appears: T-Tes t t=-2.023882612 p=.O320187274 P Value =.032019 R=-5.714285714 =-5 71429 Sx=10.56429816 n=14 m I The test statistic is t = -2.02 and the P-value is 0.032. If you specify "Draw," you see a t(13) distribution curve with the lower critical area shaded. In either case, the P-value is 0.032. -
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- ---_._ _ 11.2 Comparing Two Mea?_s,--B&--r-E T (b) A psychologist develops a test that measures social insight. He compares the social insight of male college students with that of female college students by giving the test to a sample of students of each gender. (c) A bank wants to know which of two incentive plans will most increase the use of its credit cards. It offers each incentive to a random sample of credit card customers and compares the amount charged during the following six months.
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Chapter11_2 - \ &gt; - - -11 Inference for Distributions...

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