Homework SourseUse the given information to answer parts a through d Ho u1
Use the given information to answer parts (a) through (d).
Ho: u1</=u2, a=0.025
Sample statistics: x1=2237, s1=166. n1=13
x2=2314, s2=52, n2=11
assume sigma 2/1 does not equal sigma 2/2
t0-2.228
a) Find the test statistic
b) find the standardized test stat
c) decide whether the standardized test stat is in the rejection region
d) decide whether you should reject or fail to reject the null hypothesis
Solution
2 SAMPLE T TEST (UNPOOLED)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 </= 0
Ha: u1 - u2 <= 0
At level of significance = 0.025
As we can see, this is a 1 tailed test.
Calculating the means of each group,
X1 = 2237
X2 = 2314
Calculating the standard deviations of each group,
s1 = 166
s2 = 52
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 13
n2 = sample size of group 2 = 11
Thus, df = n1 + n2 - 2 = 22
Also, sD = 48.63651395
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = -1.583172677 [ANSWER, PART A]
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[PLEASE CHECK PART B\'S QUESTION. ISN\'T THAT THE SAME AS PART A?]
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where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = -2.073873068
Thus, the rejection region is t < -2.07387. The test stat (t) is NOT IN THE REJECTION REGION. [ANSWER]
Thus, comparing t and tcrit, we decide to WE FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER, PART D]
Also, using p values,
p = 0.063826476
Comparing this to the significance level, WE FAIL TO REJECT THE NULL HYPOTHESIS.
