SOLUTION: Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the .10 level of significance, can we con

Algebra ->  Probability-and-statistics -> SOLUTION: Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the .10 level of significance, can we con      Log On


   

Question 523155: Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent?
(a) State the null hypothesis and the alternate hypothesis.
(b) What is the probability of a Type I error?
(c) Is this a one-tailed or a two-tailed test?
(d) What is the decision rule?
(e) What is the value of the test statistic?
(f) What is your decision regarding the null hypothesis?
(g) What is the p-value? Explain what it means in terms of this problem.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent.:: pa-hat = 87/150 = 0.580
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Of 200 children sampled, 123 rated it excellent.:: pc=hat = 123/200 = 0.615
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Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent?
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(a) State the null hypothesis and the alternate hypothesis.
Ho: pa-pc = 0
Ha: pa-pc is not 0
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(b) What is the probability of a Type I error?::P(Type I) = alpha = 10%
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(c) Is this a one-tailed or a two-tailed test?:::: 2-tail
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(d) What is the decision rule?:: Reject Ho is test stat <-1.645 or >+1.645
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(e) What is the value of the test statistic?:::
ts = (0.580-0.615)/sqrt[(.58*0.42/150)+(0.615*0.385/200)] = -0.6605
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(f) What is your decision regarding the null hypothesis?
Since the ts is not in a reject interval, fail to reject Ho.
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(g) What is the p-value? Explain what it means in terms of this problem.
p-valu = 2*P(z < -0.6605) = 2*0.25 = 0.50
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There is a 50% probability that the test results could have provided
stronger evidence for rejecting Ho.
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Cheers,
Stan H.
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