A researcher is interested in whether union workers earned significantly higher
ID: 3129449 • Letter: A
Question
A researcher is interested in whether union workers earned significantly higher wages than non-union workers last year. She interviewed 12 union workers and 15 non-union workers, and their wages are shown in the following table. Test the null hypothesis of no difference between the wages of union workers and non-union workers.(=0.05
Union
16.95
17.21
14.00
17.21
16.00
18.50
18.24
16.35
14.9
15.45
17.80
19.00
Non-Union
11.20
10.95
13.50
15.00
12.75
11.80
13.00
15.40
14.50
10.75
15.80
13.00
11.65
10.50
14.00
a.Formulate the null and alternative hypothesis test.
b.Calculate the p-value.
c.What is your decision? Why?
d.State the conclusion and what this represents.
Union
16.95
17.21
14.00
17.21
16.00
18.50
18.24
16.35
14.9
15.45
17.80
19.00
Non-Union
11.20
10.95
13.50
15.00
12.75
11.80
13.00
15.40
14.50
10.75
15.80
13.00
11.65
10.50
14.00
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
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b)
Calculating the means of each group,
X1 = 16.80083333
X2 = 12.92
Calculating the standard deviations of each group,
s1 = 1.515894325
s2 = 1.754260121
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 12
n2 = sample size of group 2 = 15
Thus, df = n1 + n2 - 2 = 25
Also, sD = 0.629806747
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 6.161943091
where uD = hypothesized difference = 0
Also, using p values,
p = 1.92106E-06 [ANSWER, P VALUE]
**********************************
c)
As P < 0.05, WE REJECT THE NULL HYPOTHESIS.
********************
d)
Hence, there is significant evidence at 0.05 level that there is a difference between the wages of union workers and non-union workers. [CONCLUSION]
*****************************************************
Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!
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