5.docx
A sample of 17 breakfast cereals is selected and the amount of sugar and the amount of sodium per serving (both measured in grams) are recorded. The correlation between sugar and sodium content for these cereals is calculated to be -0.434.
We would like to conduct a hypothesis test at the 1% level of significance to determine whether there exists a negative correlation between the amount of sugar and the amount of sodium in the population of all breakfast cereals.
(a) The hypotheses for the appropriate test of significance are:
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%3D-0.434]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%26gt%3B-0.434]()
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%3D-0.434]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%26lt%3B-0.434]()
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%3D0]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%26lt%3B0]()
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%3D0]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=%26rho%3B%26gt%3B0]()
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=r%3D-0.434]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=r%26lt%3B-0.434]()
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H0: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=r%3D-0.434]() vs. Ha: ![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=r%26gt%3B-0.434]()
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(b) The value of the test statistic for the appropriate test of significance (rounded to
two
decimal places) is
t = .
(c) The P-value for the appropriate test of significance is between and .
(d) If we conducted the test using the critical value method, the decision rule would be to reject H0 if
![http://angel.bfwpub.com/intellipro/geteq.ashx?eqtext=t%26le%3B]()
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(e) What is the correct conclusion for this test?
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Reject H0. There is insufficient evidence that there exists a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Fail to reject H0. There is insufficient evidence that there does not exist a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Fail to reject H0. There is sufficient evidence that there exists a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Reject H0. There is sufficient evidence that there does not exist a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Reject H0. There is insufficient evidence that there does not exist a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Fail to reject H0. There is insufficient evidence that there exists a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Reject H0. There is sufficient evidence that there exists a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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Fail to reject H0. There is sufficient evidence that there does not exist a negative correlation between the amount of sugar and the amount of sodium in breakfast cereals.
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