Question

Reserve Problems Chapter 10 Section 1 Problem 1 Your answer is partially correct. Try again. Consider the hypothesis test Ho : H1 H2 = 0) against H1 : Hi - U2 7 0 samples below: I 36 40 31 32 33 30 31 30 38 38 31 38 3731 39 31 36 38 II 32 30 33 32 32 29 30 38 32 34 30 30 31 33 34 34 Variances: j = 3.6, 02 = 2.5. 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). 2.2005 ZO P-value = 0.0278 (b) Explain how this test could be conducted with a confidence interval. Round your answers to three decimal places (e.g. 98.765). <M1-42 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 3? Round your answer to three decimal places (e.g. 98.765). The power of the test is 1-B=

Answer 1

b)

Point estimate of difference '=x1-x2 =			2.319
for 95 % CI value of z=			1.960	from excel:normsinv((1+0.95)/2)
margin of error E=z*std error =			2.066
lower bound=(x1-x2)-E =			0.25
Upper bound=(x1-x2)+E =			4.39
from above 95% confidence interval for population mean =(0.254 <µ1-µ2<4.385)

c)

rejection region : x1-x2 <=Δ+z*se or x1-x2 >=Δ+z*se or x1-x2 <=-2.0655 or x1-x2>=2.0655

P(Type II error) =P(-2.0655<x1-x2<2.0655 |Δ=3)=P((-2.0655-3)/1.0539<z<(2.0655-3)/1.0539)=P(-4.81<z<-0.89)=0.1867

P(Power) =1-type II error =1-0.1867=0.813