Z-TESTS We will use the formula for Z from lecture notes, page 2. since H 0 is u
ID: 3153626 • Letter: Z
Question
Z-TESTS
We will use the formula for Z from lecture notes, page 2.
since H0 is usually m1=m2, then m1-m2= 0 and:
for 1, 2 known
for 1, 2 unknown
Z = if n1 + n2 32
Steps to be covered:
State the hypotheses, and identify the claim
Find the critical value(s) – you might want to draw the curve
Compute the test (statistic) value
Make the decision to reject or not reject the null hypothesis.
PROBLEM 7:
Are the contributions statistically significant equal? Test at .01 significance level
Men: Average gross income = $48,500; standard deviation = $1,000;
n = 18 employees
Women: Average gross income = $43,600; standard deviation = $2,000;
n = 11 employees
Explanation / Answer
7.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0 [CLAIM]
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At level of significance = 0.01
As we can see, this is a two tailed test.
Now, the critical value for t is
df = n1 + n2 - 2 = 27
tcrit = +/- 2.770682957 [ANSWER, CRITICAL VALUES]
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Calculating the means of each group,
X1 = 48500
X2 = 43600
Calculating the standard deviations of each group,
s1 = 1000
s2 = 2000
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 18
n2 = sample size of group 2 = 11
Also, sD = 647.4503218
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 7.568148219 [ANSWER, TEST STATISTIC]
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As |t| > 2.771, WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that the contributions are not equal. [CONCLUSION]
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