Question

Consider the hypothesis test  H0: μ1-μ2=0 against  H1: μ1-μ2≠0 samples below:

Reserve Problems Chapter 10 Section 1 Problem 1 Consider the hypothesis test HO : H1 - H2 = 0 against HL : M - H270 samples below: I 35 38 31 32 33 30 31 29 39 38 30 37 37 30 39/32 3540 II |32|30|34|33|31|29 30 37 31 33 30 29 29 33 34 35 Variances: 0 = 3.9, 02 = 2.7. Use a = 0.05. (a) Test the hypothesis and find the P-value. Find the test statistic. Round your answers to four decimal places (e.g. 98.7654). ZON P-value = (b) Explain how this test could be conducted with a confidence interval. Round your answers to three decimal places (e.g. 98.765). ISH - H2S We are 95% confident that value 1 exceeds value 2 by between (c) What is the power of the test for the true difference in means of 2? Round your answer to three decimal places (e.g. 98.765). The power of the test is 1-B =

Answer 1

Ans: 0 = 3.9, 62 = 2.7 ny = 18 M2 = 16 34.22-31.88 2.0518 31ge 2.72 18 my P value = -222 van Giren, Ho: 41-42=0 against th: 11-1270 Boy Calculating, weget ti = 34122 j5 = 31.88 $ =005 Test statistic Zoo 4 - Xe 522 + site 0.0402 As pralue < 0.0529, So Reject tto. 6) for the for tee 95% Cortidence intenval Lodz 1996. - The 95%. Catidence interral is (34.22 - 31:88) - 1.96 <Hi 82 3(34.22-31188) +1696/8 0.105 3/4-A2 < 4.575 with 95% Confidence the troue difference in the means in between 0.105 and 4.575. Because zero is not Contained in this interral, we concludes there is a significant difference between the means we reject the mall hypothesis. ay 3192 + 2.7² 18 16 i 0 2 are love, p= 4/2012 - 4 = 4(16 off- + [ 0.21] -4 -31) -1.96 3192 2.7² 18 76 - 0.00010 0.58317 0.58307 power = 1-6 = -0.58307 417