Question

he null and alternate hypotheses are:

H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂

A random sample of 11 observations from one population revealed a sample mean of 24 and a sample standard deviation of 4.6. A random sample of 8 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.1.

At the 0.05 significance level, is there a difference between the population means?

1. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)

3. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. State your decision about the null hypothesis.

• Reject H₀.

• Do not reject H₀.

5. The  p-value is

• between 0.05 and 0.02

• less than 0.001

• between 0.05 and 0.1

• between 0.001 and 0.01

• between 0.1 and 0.2

Answer 1

a)

degree of freedom   v=	(n1+n2-2)=	17.000
for 0.05 level ,two tail test &17 df, critical t=	2.110
Decision rule :                   reject Ho if absolute value of test statistic |t|>2.110

b)

Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=

19.369

c)

Point estimate : x1-x2=		-5.0000
standard error se =Sp*√(1/n1+1/n2)=	2.0450
test stat t =(x1-x2-Δo)/Se=	-2.445

d)

Reject H0.

e)

between 0.05 and 0.02