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# Z-test and independent t-test: assumptions, theory, and calculations (Example)

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Student’s Name Instructor’s Name Course Date Z-test and independent t-test: assumptions theory and calculations Question 1 90 percent confidence n1 = 11 n2= 18 x 1 = 744 x 2 = 299 σ21 = 62 σ22 = 32 Since the variance is known the 1001-α percent confidence interval for μ1-μ2 is given by ( x 1 - x2 )± z(1-α2)√( σ21)/ n1 + (σ22/ n2) ( x 1 - x2 ) = 744 – 299 = 445 √( 62/18) + (32/11) = 2.521 445± 1.645(2.521) (440.9 449.1) The difference between the two population (lean and obese) means is 445 and the researchers are 90% confident that the true mean lies between 440.9 and 449.1. 95 two populations are equal the point of estimate is given by ( x 1 - x2 ) = 20.6 – 17.4= 3.2 The pooled estimate of the variance is given by σ2 P ={(n1-1)σ21+(n2-1) σ22}/(n1+n2-2) σ2 P ={185-15.8+(86-1) 5.8}/(185+86-2) σ2 P=(18433.64+85(33.64))/270σ2 P = 33.52 The standard error is given by (33.52186+33.5286) = The 99% confidence interval is then given as 3.2±t(1.960) (33.52186+33.5286) 3.2±2.576(0.755) (1.3 5.1) The correct value of t to use for a 95% confidence interval with 270 degrees of freedom is 2.576.  We interpret this interval that the difference between the two population means is estimated to be 3.2 and we are 99% confident that the true value lies between 1.3 and 5.1 [...]

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