Question

Chapter 10 Section 1 Additional Problem 1 Your answer is partially correct. Try again. Consider the hypothesis test Ho : 41 = 112 against Hp : \l] <H2 with known variances 01 = 11 and 62 = 6. Suppose that sample sizes nj = 10 and n2 = 16 and that īj = 14.4 and 12 = 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 Mi is 4 units less than uz? (C) Assuming equal sample sizes, what sample size should be used to obtain B = 0.05 if u 1 is 4 units less than 42 ? Assume that a = 0.05. (a) The null hypothesis is notv rejected. The P-value is 0.0770 Round your answer to four decimal places (e.g. 98.7654). 0.10 (b) The power is Round your answer to two decimal places (e.g. 98.76). 107 (c)n = 12 Round your answer up to the nearest integer. Stati:

Answer 1

b)

Hypothesized mean difference Δo       =			0
true mean difference Δ                                                          =			-4
first sample standard deviation =σ1    =			11.000
second sample std deviation =σ2=			6.000
first sample size =n1 =			10.000
second sample size =n2 =			16.000
standard error=(√(σ12/n1+σ12/n1))=			3.7881
for 0.05 level and left tail critival Zα=			-1.64
rejecf Ho if x<= Δo +Zα*σx or x<=			-6.2125
P(Type II error) =P(Xbar>-6.213| Δ=-4)=P(Z>(-6.2125--4)/3.788)=P(Z>-0.58)=0.719
P(Power) =1-type II error =1-0.719=0.28