Question

The null and alternate hypotheses are:

H0 : μ1 = μ2

H1 : μ1 ≠ μ2

A random sample of 11 observations from Population 1 revealed a sample mean of 21 and sample deviation of 3.5. A random sample of 7 observations from Population 2 revealed a sample mean of 23 and sample standard deviation of 3.8. The underlying population standard deviations are unknown but are assumed to be equal.

At the .05 significance level, is there a difference between the population means?

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

The decision rule is to reject H0 if t <  or t > .

(b)	Compute the pooled estimate of the population variance. (Carry at least 3 decimal places in all intermediate calculations. Round your answer to 3 decimal places.)

Pooled estimate of the population variance

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

Test statistic

(d)	State your decision about the null hypothesis.
	(Click to select)Do not rejectReject H0 .

Answer 1

a)

This is two tailed test, for α = 0.05 and df = n1 + n2 - 2 = 16
Critical value of t are -2.12 and 2.12.
Hence reject H0 if t < -2.120 or t > 2.120

b)

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((11 - 1)*3.5^2 + (7 - 1)*3.8^2)/(11 + 7 - 2))*(1/11 + 1/7))
sp = 1.748

c)

Test statistic,
t = (x1bar - x2bar)/sp
t = (21 - 23)/1.748
t = -1.144

d)

Do not Reject H0 .