Question

Consider the hypothesis test Ho: Mi = u2 against Hui < u2 with known variances 01 = 10 and 02 = 6. Suppose that sample sizes nj = 11 and n2 = 14 and that Ij = 14.3 and I2 = 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 fi is 4 units less than 12? (C) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if u1 is 4 units less than 112? Assume that a = 0.05. (a) The null hypothesis rejected. The P-value is Round your answer to four decimal places (e.g. 98.7654). (b) The power is Round your answer to two decimal places (e.g. 98.76). (c) ni = n2 = Round your answer up to the nearest integer. Statistical Tables and cl

Answer 1

a)

		pop 1	pop 2
sample mean x =		14.30	19.60
std deviation σ=		10.000	6.000
sample size n=		11	14
std error σx1-x2=√(σ21/n1+σ22/n2)    =			3.415
test stat z =(x1-x2-Δo)/σx1-x2     =			-1.55
p value : =			0.0606	(from excel:1*normsdist(-1.55)

the null hypothesis is not rejected , the p value is 0.0606

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