Question

Consider the hypothesis test Ho: Mi = H2 against H:M1 < u2 with known variances a = 10 and 02 = 6. Suppose that sample sizes ni = 11 and 12 = 14 and that īj = 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 1 is 4 units less than 42? (c) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if y1 is 4 units less than u2? 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)n = n2 = Round your answer up to the nearest integer.

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 ; p value =0.0606

b)

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