Question

Chapter 10 Section 1 Additional Problem 1 Your answer is partially correct. Try again. Consider the hypothesis test Ho: M1 = 42 against H:41 <H2 with known variances 01 = 11 and O2 = 6. Suppose that sample sizes nj = 10 and n2 = 16 and that Ãj = 14.4 and 2 = 19.8. 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 u is 4 units less than plz? (c) Assuming equal sample sizes, what sample size should be used to obtain p = 0.05 if H1 is 4 units less than 42? Assume that a = 0.05. 10.1540 (a) The null hypothesis is not 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 106 Round your answer up to the nearest integer.

Answer 1

a)

		pop 1	pop 2
sample mean x =		14.40	19.80
std deviation σ=		11.000	6.000
sample size n=		10	16
std error σx1-x2=√(σ21/n1+σ22/n2)    =			3.788
test stat z =(x1-x2-Δo)/σx1-x2     =			-1.43
p value : =			0.0764	(from excel:1*normsdist(-1.43)

b)

for 0.05 level and left tail critival Zα=			-1.645
rejecf Ho if x<= Δo +Zα*σx or x<=			-6.2315
P(Type II error) =P(Xbar>-6.232| Δ=-4)=P(Z>(-6.2315--4)/3.788)=P(Z>-0.59)=0.7224
P(Power) =1-type II error =1-0.7224=0.28