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# ch10 - Chapter Ten 10.1 The two samples are independent if...

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Chapter Ten 10.1 The two samples are independent if they are drawn from two different populations and the elements of the two samples are not related. As an example, suppose we want to estimate the difference between the salaries of male and female university professors. To do so, we will select two samples from two different populations, one from all male university professors and the second from all female university professors. These two populations will include different elements that are not related. In two dependent samples, the elements of one sample are related to the elements of the second sample. To test if a certain course that claims to reduce stress, does indeed decrease stress, we will take a sample of people who are suffering from stress. We will measure the stress level for these people before they take this course and then after they finish it. Based on these results we will make a decision. Notice, that in this example, we have the same group of people for two samples of data, one before taking the course and the second after completing the course. 10.3 a. The point estimate of μ 1 μ 2 is 2 1 x x - = 5.56 – 4.80 = .76 2 1 x x s - = = + 2 2 2 1 2 1 n s n s = + 270 ) 58 . 1 ( 240 ) 65 . 1 ( 2 2 .14349103 Margin of error = 28 . ) 14349103 (. 96 . 1 96 . 1 2 1 ± = ± = ± - x x s b. The z value for the 99% confidence level is 2.58. The 99% confidence interval for μ 1 μ 2 is: 2 1 ) ( 2 1 x x zs x x - ± - = .76 ± 2.58 (.14349103) = 0.76 ± .37 = .39 to 1.13 TI-83 : Select STAT, TESTS, 9: 2-SampZInt, and press the ENTER key. If you have summary statistics highlight Stats otherwise select Data. Here we have summary statistics and will choose Stats and press the ENTER key. We then use the down arrow to scroll down to enter the requested information for the first sample followed by the information from the second sample. In this example its 1 x = 5.56, σ1= s 1 = 1.65, n 1 = 240, 2 x = 4.80, σ2= s 2 = 1.58, n 2 = 270, C-Level: = .99 for the Confidence level, highlight No for pooled data, highlight Calculate, and press the ENTER key. 187

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188 Chapter Ten  SampZInt (.39039, 1.1296) = 1 x 5.56 = 2 x 4.8     n 1  = 240     n 2  = 270 10.5 H 0 : μ 1 μ 2 = 0; H 1 : μ 1 μ 2 ≠ 0 For α = .05, the critical values of z are –1.96 and 1.96. From Exercise 10.3, 2 1 x x s - = .14349103 = - - - = - 2 1 ) ( ) ( 2 1 2 1 x x s x x z μ μ 30 . 5 14349103 . 0 ) 80 . 4 56 . 5 ( = - - Reject H 0 . TI-83 : Select STAT, TESTS, 3: 2-SampZTest, and press the ENTER key. If you have summary statistics highlight Stats otherwise select Data. Here we have summary statistics and will choose Stats and press the ENTER key. We then use the down arrow to scroll down to enter the requested information for the first sample followed by the information from the second sample. In this example its σ1= s 1 = 1.65, σ2= s 2 = 1.58, 1 x = 5.56, n 1 = 240, 2 x = 4.80, n 2 = 270, for μ 1 highlight ≠ μ 2 as this is a two tailed test, highlight Calculate, and press the ENTER key. The results are shown below and from them we can see that in this example we reject the null hypothesis.
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ch10 - Chapter Ten 10.1 The two samples are independent if...

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