1st drop down Reject or do not reject2nd drop down Is evidence o.pdf
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The document discusses a hypothesis testing scenario comparing two population proportions. It formulates null and alternative hypotheses, calculates the z-statistic, and determines a rejection region to conclude that there is significant evidence indicating increased effort to get removed from a mailing list. The result supports the claim of this increased difficulty.
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![1st drop down: Reject or do not reject
2nd drop down: Is evidence or is insufficient evidence
3rd drop down: Yes or No
4th drop down: Makes or does not make
Solution
a)
Ho: pi1<= pi2
Ha: pi1 > pi2 [ANSWER, OPTION D]
*************
B)
Formulating the hypotheses
Ho: p1^ - p2^ <= 0
Ha: p1^ - p2^ > 0
Here, we see that pdo = 0 , the
hypothesized population proportion difference.
Getting p1^ and p2^,
p1^ = x1/n1 = 0.34
p2 = x2/n2 = 0.2
Also, the standard error of the difference is
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.062
Thus,
z = [p1 - p2 - pdo]/sd = 2.258064516 = 2.258 [ANSWER, PART B]
*************************************
As significance level = 0.05 , then the critical z is
zcrit = 1.644853627](https://image.slidesharecdn.com/1stdropdownrejectordonotreject2nddropdownisevidenceo-230703055758-46cb5838/85/1st-drop-down-Reject-or-do-not-reject2nd-drop-down-Is-evidence-o-pdf-1-320.jpg)
![Thus, the rejection region is ZSTAT > 1.645 [ANSWER, OPTION ]
****************************************
Thus comparing z > zcrit, WE REJECT THE NULL HYPOTHESIS.
There is evidence that it takes more effort now to get removed from a mail list than before.
***************************
c)
Yes, the result in b) makes it appropriate to claim it.](https://image.slidesharecdn.com/1stdropdownrejectordonotreject2nddropdownisevidenceo-230703055758-46cb5838/85/1st-drop-down-Reject-or-do-not-reject2nd-drop-down-Is-evidence-o-pdf-2-320.jpg)
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1st drop down Reject or do not reject2nd drop down Is evidence o.pdf
- 1. 1st drop down: Reject or do not reject 2nd drop down: Is evidence or is insufficient evidence 3rd drop down: Yes or No 4th drop down: Makes or does not make Solution a) Ho: pi1<= pi2 Ha: pi1 > pi2 [ANSWER, OPTION D] ************* B) Formulating the hypotheses Ho: p1^ - p2^ <= 0 Ha: p1^ - p2^ > 0 Here, we see that pdo = 0 , the hypothesized population proportion difference. Getting p1^ and p2^, p1^ = x1/n1 = 0.34 p2 = x2/n2 = 0.2 Also, the standard error of the difference is sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.062 Thus, z = [p1 - p2 - pdo]/sd = 2.258064516 = 2.258 [ANSWER, PART B] ************************************* As significance level = 0.05 , then the critical z is zcrit = 1.644853627
- 2. Thus, the rejection region is ZSTAT > 1.645 [ANSWER, OPTION ] **************************************** Thus comparing z > zcrit, WE REJECT THE NULL HYPOTHESIS. There is evidence that it takes more effort now to get removed from a mail list than before. *************************** c) Yes, the result in b) makes it appropriate to claim it.