Z-TESTS We will use the formula for Z from lecture notes, page 2. since H 0 is u
ID: 3153628 • 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 4:
Is there a statistically significant difference between the salaries of the two sets?
Test at .02 significance level.
High school graduates: Average salary = $35,000; standard deviation = $15,000; n = 100
High school dropouts: Average salary = $26,000; standard deviation = $10,000; n = 75
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0 [CLAIM]
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At level of significance = 0.02
As we can see, this is a two tailed test.
Hence, the critical z values are
zcrit = -2.33, 2.33 [ANSWER]
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Calculating the means of each group,
X1 = 35000
X2 = 26000
Calculating the standard deviations of each group,
s1 = 15000
s2 = 10000
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 100
n2 = sample size of group 2 = 75
Also, sD = 1892.969449
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = 4.754434894 [ANSWER, TEST STATISTIC]
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where uD = hypothesized difference = 0
As |z| > 2.33, WE REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence that there is a difference between the salaries of the two sets at 0.02 level. [CONCLUSION]
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