Question

Chapter 10 Section 1 Additional Problem 1 Your answer is partially correct. Try again. Consider the hypothesis test Hi : Mi = u2 against Hp : Mi <H2 with known variances (j = 10 and 62 = 6. Suppose that sample sizes nj = 11 and 12 = 14 and that j = 14.3 and 12 = 19.6. Use a = 0.05. (a) Test the hypothesis and find the P-value. (b) What is the power of the test in part (a) if p1 is 4 units less than u2? (c) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if 1 is 4 units less than 12? Assume that a = 0.05. 0.0606 (a) The null hypothesis is not rejected. The P-value is Round your answer to four decimal places (e.g. 98.7654). 0.75 (b) The power is Round your answer to two decimal places (e.g. 98.76). X 67 (c) ni = n2 = Round your answer up to the nearest integer. Statistical Tables and Charts

Answer 1

b)

Hypothesized mean difference Δo       =			0
true mean difference Δ                                                          =			-4
first sample standard deviation =σ1    =			10.000
second sample std deviation =σ2=			6.000
first sample size =n1 =			11.000
second sample size =n2 =			14.000
standard error=(√(σ12/n1+σ12/n1))=			3.4150
for 0.05 level and left tail critival Zα=			-1.645
rejecf Ho if x<= Δo +Zα*σx or x<=			-5.6177
P(Type II error) =P(Xbar>-5.618| Δ=-4)=P(Z>(-5.6177--4)/3.415)=P(Z>-0.47)=0.6808
P(Power) =1-type II error =1-0.6808=0.32

c)

Hypothesized mean difference Δo       =			0
true mean difference =Δ =			4
first sample std deviation =σ1   =			10.000
2ndsample std deviation=σ2 =			6.000
for 0.05 level and right tail critical Zα=			1.645
for 0.05 level of type II error critival Zβ=			1.645
n=(Zα/2+Zβ)2(σ12+σ22)/(Δo-Δ)2 =			93