Solve the problem by carefully answering the following questions: 1. State the p
ID: 3151360 • Letter: S
Question
Solve the problem by carefully answering the following questions: 1. State the pair of the null and the alternative hypotheses. 2. Is this a one-tailed or two-tailed test? 3. Is it the testing of the dependent or independent populations/samples? 4. What is the decision rule? 5. State the data on each sample. 6. What is the value of the test-statistic? 7. What is the p-value? 8. What is your decision regarding the null hypothesis? 9. Explain your decision in the terms of the problem/provided situation. B. Of 150 adults who tried a new peach-flavored peppermint Pattie, 87 rated it as excellent. Of 200 children sampled, 123 rated it as excellent. Using the significance level of 0.10, can we conclude that there is a significant difference in the proportions of adults and children who all rated the new flavor as excellent?Explanation / Answer
1.
Formulating the hypotheses
Ho: p1 - p2 = 0
Ha: p1 - p2 =/= 0 [ANSWER]
2. TWO TAILED TEST
3. INDEPENDENT SAMPLES
4. As alpha = 0.10 two tailed,
Reject Ho when |z| > 1.645. [ANSWER]
5.
x1 = 87
n1 = 150
x2 = 123
n2 = 200
6.
Here, we see that pdo = 0 , the hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 0.58
p2 = x2/n2 = 0.615
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.052989386
Thus,
z = [p1 - p2 - pdo]/sd = -0.660509638 [ANSWER]
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7.
Also, the p value is, as this is two tailed,
P = 0.508926835 [ANSWER]
8.
As P > 0.10, we FAIL TO REJECT HO.
9.
Thus, there is no significant evidence that the proportions of adults and children who rated the new flavor as excellent differ at 0.10 level. [CONCLUSION]
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