Question

	A sample of starting salaries for bachelor degree level graduates in two different cities showed the following:
					City 1			City 2
n	sample count				35			30
xbar	sample average				60,000			58,000
s	sample standard deviation				5,000			6,000
	We do not know any population means or population standard deviations.
	Using alpha = .01   test whether the population average starting salaries are different.

Answer 1

Since s₁/s₂ = 5000 / 6000 = 0.83 (it lies between 0.5 and 2) we used the pooled variance.

The degrees of freedom used is n1 + n2 - 2 = 35 + 30 - 2 = 63 (since pooled variance is used)

The Hypothesis:

H0:

Ha:

This is a Two tailed test.

The Test Statistic:We use the students t test as population standard deviations are unknown.

The p Value:    The p value (2 Tail) for t = 1.47, df = 63, is; p value = 0.1476

The Critical Value:   The critical value (2 tail) at = 0.01,df = 63, t critical = +2.656 and -2.656

The Decision Rule: If t observed is > t critical or If   t observed is < -t critical, Then Reject H0.

Also If the P value is < , Then Reject H0

The Decision: Since t lies in between +2.656 and -2.656, We Fail To Reject H0

Also since P value (0.1476) is > (0.01), We Fail to Reject H0.

The Conclusion: There isn't sufficient evidence at the 99% significance level to conclude that the population average starting salaries are different in City 1 and City 2.