Question 146066: Do a larger proportion of college students than young children eat cereal? Researchers surveyed both age groups to find the answer. The results are shown in the table below. (a) State the hypotheses used to answer the question. (b) Using α = .05, state the decision rule and sketch it. (c) Find the sample proportions and z statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f) Is the normality assumption fulfilled? Explain
Statistic College Students (ages 18–25) Young Children (ages 6–11)
Number who eat cereal x1 = 833 x2 = 692
Number surveyed n1 = 850 n2 = 740
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Do a larger proportion of college students than young children eat cereal? Researchers surveyed both age groups to find the answer. The results are shown in the table below.
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Statistic College Students
........ (ages 18–25) Young Children (ages 6–11)
Number who eat cereal x1 = 833 x2 = 692
Number surveyed...... n1 = 850 n2 = 740--------
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(a) State the hypotheses used to answer the question.
Ho: p(college) - p(youngsters) = 0
Ha: p(college) - p(youngsters) > 0
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(b) Using α = .05, state the decision rule and sketch it.
Reject Ho if z> 1.645
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(c) Find the sample proportions and z statistic.
p1-hat = 833/850 = 0.98.. ; p2-hat = 692/740 = 0.9351...
p-bar = (833+692)/(850+740) = 0.95912..
I ran a 2-proportion Z-test on a TI calculator to get:
z(0.98-09351) = 4.50649...
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(d) Make a decision.
Since 4.50649.. is greater than 1.645, reject Ho.
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(e) Find the p-value and interpret it.
p-value = 0.000003298...
Only that percentage of test results could have resulted in stronger
evidence for rejecting Ho.
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(f) Is the normality assumption fulfilled? Explain
I'll leave that to you.
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Cheers,
Stan H.
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