Question 1172147: CASE STUDY 1 TO ANSWER QUESTIONS 1 AND 2
A company claims that its best-selling product contains more than 40 qualities. This claim is tested at 1% significance. Evidence suggests that the product is normally distributed. Information from a computer output of the hypothesis test is listed as follows.
Sample mean = 42.6
P-value = 0.008
Sample standard deviation = 3.7
Sample size = 15.
Test statistic t = 2.72155
Critical value t = 2.62610
Use it to answer question 1 and 2
Question 1
a) Is this a right-tailed, left-tailed, or two-tailed test? Explain in one sentence. Draw a graph to support your type of test. Determine the claim.
b) From the observed P-value, what would you conclude and why? What if the significance value is 0.5% and the p- value remains the same?
c) By comparing the test statistic to the critical value, what would you conclude and why?
d) Is there a conflict in this output? Explain in one sentence. What would have been the other alternative and why should it be so?
Question 2
a) Is this a large or a small sample test? Explain the other alternative.
b) ‘This claim is tested at 1% significance level’. Explain this statement to a colleague who did not do MATH 203.
c) What has been proved in this study?
d) How is this P - value arrived at?
e) How is the sample mean arrived at? Give an example of a sample size of three.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If you look at t cdf for -2.72, +2.72, 14, it is 0.9834. That is missing 0.0166 and with a two-way test, the p-value would be that 0.0166. It is instead 0.008, so this is a one-way test. Compare with the one way cdf using 2.72155, 20 (or a larger number), 14, which is 0.008.
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Conclude there is a significant difference. If the significance value is 0.005, one would fail to reject.
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1% significance for a one-way test is not the same p-value as for a two-way test, where the one way p-value is doubled. Yet to me the question reads more than 40 and certainly could qualify for a one way test. A 1% significance for a two way test has a larger t-value, nearly 3, and would fail to reject Ho here.
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Small sample, because it is not >30. Note, sampling from normal distributions produces normal distributions, but if it is not clear that it is normal (and "suggests" could be taken to mean it isn't clear), then the t-test should be used. Usually with small samples, where the sd used is taken from the sample, a t-test will be used. Sample sizes >30 from skewed populations may not qualify to be normal.
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The 1% significance level means that if there were no difference, between the sample and the population, we would expect to see a result this extreme or more so 1% of the time. The p-value was arrived at by looking at the upper level of the df=14 t-distribution. If we wanted to make it a two-way test, as said above, we would double the p-value.
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