A sample of 40 observations is selected from one population with a population st
ID: 3157614 • Letter: A
Question
A sample of 40 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 100.0. A sample of 55 observations is selected from a second population with a population standard deviation of 4.6. The sample mean is 98.6. Conduct the following test of hypothesis using the 0.10 significance level.
State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)
A sample of 40 observations is selected from one population with a population standard deviation of 3.3. The sample mean is 100.0. A sample of 55 observations is selected from a second population with a population standard deviation of 4.6. The sample mean is 98.6. Conduct the following test of hypothesis using the 0.10 significance level.
H0 : 1 = 2 H1 : 1 2Explanation / Answer
a)
As H1 used =/= , it is TWO TAILED TEST.
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b)
As it is 0.10 level, two tailed,
Reject Ho if z is outside the interval (-1.65, 1.65). [ANSWER]
[The more exact answer is (-1.6449, 1.6449), but many go for 1.65. Please feel free to use 1.64 if that's what you use in class.]
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c)
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.1
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 100
X2 = 98.6
Calculating the standard deviations of each group,
s1 = 3.3
s2 = 4.6
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 40
n2 = sample size of group 2 = 55
Also, sD = 0.810541345
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = 1.727240699 [ANSWER]
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d)
As z > 1.645, REJECT HO. [ANSWER]
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e)
Using table/technology, as this is two tailed,
Pvalue = 0.084124444 [ANSWER]