Question

Unless otherwise noted, a= .05

16 The authors Problem 5 (5 points): You find a report about the relationship between education and income. surveyed 36 participants and asked their income and their level of education achieved. Among those participants who had completed a college degree (n 18), the mean income was $35 per hour and the sample variance was 81. Among those participants who had not completed a college degree (n -18), the mean income $25 per hour and the sample standard deviation was 81. Test the hypothesis that income was related to college degree.

Answer 1

Let's denote the data for participants holding a degree with subscript 1 and for those without a degree by 2.

Data given is as follows:

Sample sizes, n1 = 18, n2 = 18

Sample means, m1 = 35, m2 = 25

Sample SD's, s1 = 81^0.5 = 9, s2 = 81^0.5 = 9

Hypotheses are stated as:

H0: $\mu$ 1 = $\mu$ 2

Ha: $\mu$ 1 $\neq$ $\mu$ 2

Next calculate the standard error:

S' = ((s1^2)/n1 + (s2^2)/n2)^0.5 = ((9^2)/18 + (9^2)/18)^0.5 = 3

Now we calculate test statistic:

t = (m1-m2)/S' = (35-25)/3 = 3.33

Degrees of freedom = n1+n2-2 = 34

The corresponding p-value is:

p = 0.0021

Significance level, a = .05

Since this is a two tailed test we compare p with a/2.

Since p < a/2, so we have to reject the null hypothesis.

So there is significant evidence that $\mu$ 1 $\neq$ $\mu$ 2.

This means that degree and income are indeed related.