Question 136080: Can someone help me with these 2 problems. My instructor asked this question and I have no clue as to what is going on here. Thanks In Advance.
1. Imagine this scenario at your marketing department ..
You have been given the task of showing that there is a difference between gender and potato chip preferences.
A colleague has obtained some sample data for you:
Lays Jays Better Maid Private Label
Male 16 6 5 10
Female 7 4 11 7
>> how will you proceed ??
2. To test the hypothesis that students who finish an exam first get better grades. Professor Hardtack kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with the standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at a= .05? (a) State the hypothesis for a right -tailed test. (b) Obtain a test statistic and p-value assuming equal variances. Interprest these results. (c) Is the difference in mean scores large enough to be important> (d) Is it reasonable to assume equal variances? (e) Carry out a formal test for equal variances at a-.05, showing all steps clearly
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Imagine this scenario at your marketing department ..
You have been given the task of showing that there is a difference between gender and potato chip preferences.
A colleague has obtained some sample data for you:
...........Lays....Jays ...Better-Maid..... Private-Label....Row Totals
Male........16....... 6..... 5..................10.............37
Female...... 7........4......11..................7.............29
column totals23.......10......16..................17............66
>> how will you proceed ??
Determine the expected number of choices for EACH data box
as [(row total)/(grand total)]*(column total)
----------
Subtract the expected value from the given data value in each box.
Do the Male selections seem to be very different than the expected value?
Do the Female selections seem to be very different?
Can you compare them?
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2. To test the hypothesis that students who finish an exam first get better grades. Professor kept track of the order in which papers were handed in. The first 25 papers showed a mean score of 77.1 with the standard deviation of 19.6, while the last 24 papers handed in showed a mean score of 69.3 with a standard deviation of 24.9. Is this a significant difference at a= .05?
(a) State the hypothesis for a right -tailed test.
Ho: u(early)-u(later)=0
Ha: u(early)-u(later)> 0
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(b) Obtain a test statistic and p-value assuming equal variances. Interprest these results.
Run a 2-Sample T-Test to get:
test statistic: t = 1.2212
p-value = 0.1141...
Since p-value is greater than 5%, Fail to Reject Ho.
The professor is wrong.
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(c) Is the difference in mean scores large enough to be important
The test says "no".
----------------------------->
(d) Is it reasonable to assume equal variances?
Ho: (s(early))^2 = (s(later))^2
Ha: they are not equal
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F-score critical values :0.44 and 2.27
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Test statistic: F = 19.6^2/24.9^2 = 0.6196...
------------------------
Conclusion: Since test stat is not in either rejection interval, Fail to
reject Ho.
Statistically speaking, the variances are not different.
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Cheers,
Stan H.
(e) Carry out a formal test for equal variances at a-.05, showing all steps clearly
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