16 Jan Assume that we conduct
Question 1 (1 point)
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Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 230 alumni respond to our survey, 150 GA Tech graduates and 80 KSU graduates. From this survey we construct the following income data: GA Tech graduates (150 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (80 responders), average income 64,000, and the standard deviation is 15,000.
If we assume that the two population standard deviations are UNKNOWN BUT ASSUMED TO BE EQUAL (after all these are graduates with similar degrees from GA public colleges who graduated roughly during the same time period) and decide to perform a pooled variance hypothesis test for the equality of the population average incomes, what would the pooled variance be for the test (rounded to the nearest integer)?
Question 2 (1 point)
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Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 230 alumni respond to our survey, 150 GA Tech graduates and 80 KSU graduates. From this survey we construct the following income data: GA Tech graduates (150 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (80 responders), average income 64,000, and the standard deviation is 15,000.
Assume that the two population standard deviations are UNKNOWN AND CAN’T BE ASSUMED EQUAL. Please conduct a hypothesis test for the equality of the two population means (average incomes of the two groups: GA Tech and KSU graduates) with 90% significance. Would you reject the null hypothesis of the equality of the two means?
Question 3 (1 point)
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Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 230 alumni respond to our survey, 150 GA Tech graduates and 80 KSU graduates. From this survey we construct the following income data: GA Tech graduates (150 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (80 responders), average income 64,000, and the standard deviation is 15,000.
Assume that the two population standard deviations are UNKNOWN AND CAN’T BE ASSUMED EQUAL. If we conduct a hypothesis test for the equality of the two population means (average incomes of the two groups: GA Tech and KSU graduates) with 90% significance, what would the DEGREES OF FREEDOM for the test statistic be?
Question 4 (1 point)
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Assume that we conduct a survey of KSU and GA Tech business school alumni. In total, 30 alumni respond to our survey, 15 GA Tech graduates and 15 KSU graduates. From this survey we construct the following income data: GA Tech graduates (15 responders), average income 71,000, and the standard deviation is 12,000; KSU graduates (15 responders), average income 64,000, and the standard deviation is 15,000.
Assume that the two population standard deviations are UNKNOWN AND CAN’T BE ASSUMED EQUAL. Please conduct a hypothesis test for the equality of the two population means (average incomes of the two groups: GA Tech and KSU graduates) with 95% significance. Would you reject the null hypothesis of the equality of the two means?
Question 5 (1 point)
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Please use the dataset below to conduct a hypothesis test for the equality of the two population means. Please do so with 95% significance. Also assume that the two population standard deviations are unknown and cannot be assumed to be equal.
Please report the t-test statistic from your test.
Sample 1
Sample 2
38
41
36
35
36
38
37
40
38
39
37
36
35
37
37
36
40
Question 6 (1 point)
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Which of the tests listed in the answer choices will reject the hypothesis that the two population means are equal?
Please note that we don’t know the two sigmas and can’t assume that they are equal.
Sample 1
Sample 2
38
41
36
35
36
38
37
40
38
39
37
36
35
37
37
36
40
Question 7 (1 point)
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The table below reports sample statistics for two samples. Assume that we don’t know the two population standard deviations and we can’t assume that they are equal. Please conduct a 90% significance test for the equality of the two population means.
Sample1
sample 2
n
80
60
standard deviation
18
12
sample average
83
87
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