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A direct mail appeal for contributions from a university's alumni and supporters is considered to be too costly if less than 16 % of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 321 people on the alumni and supporters mailing lists. They receive monetary contributions from 42 people. Does this evidence demonstrate that the direct mall campaign is not cost effective? Use a 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer E Tables E Keypad Keyboard Shortcuts O we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost effective. O We reject the null hypothesis and conclude that there is insufficient evidence ata 0.05 level of significance that the direct mail campaign is not cost effective. O we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 ievel of significance that the direct mail campaign is not cost effective. O we reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost effective.

A direct mail appeal for contributions from a university's alumni and supporters is considered to be too costly if less than 16 % of the alumni and supporters provide monetary contributions. To determine if a direct mail appeal is cost effective, the fundraising director sends the direct mail brochures to a simple random sample of 321 people on the alumni and supporters mailing lists. They receive monetary contributions from 42 people. Does this evidence demonstrate that the direct mall campaign is not cost effective? Use a 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. Answer E Tables E Keypad Keyboard Shortcuts O we fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost effective. O We reject the null hypothesis and conclude that there is insufficient evidence ata 0.05 level of significance that the direct mail campaign is not cost effective. O we fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 ievel of significance that the direct mail campaign is not cost effective. O we reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost effective.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Analysis: Cost-Effectiveness of a Direct Mail Campaign** **Context:** A university wishes to evaluate the cost-effectiveness of its direct mail appeal for contributions from alumni and supporters. Historically, the campaign is deemed too costly if fewer than 16% of the recipients contribute monetarily. An initiative was launched where the director sent out direct mail brochures to a random sample of 321 people from the alumni and supporter mailing lists. This resulted in contributions from 42 individuals. The goal is to determine if this data supports the conclusion that the direct mail campaign is not cost-effective. The analysis is conducted at a 0.05 level of significance. **Step 3 of 3: Conclusion and Interpretation** **Answer Options:** - Option A: We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option B: We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option C: We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option D: We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. **Explanation:** The task is to decide whether the statistical evidence is strong enough to reject the null hypothesis regarding the campaign's cost-effectiveness. An appropriate choice involves assessing whether the sample contribution rate significantly diverges from the 16% benchmark, using statistical testing methods like the z-test for proportions.
Transcribed Image Text:**Analysis: Cost-Effectiveness of a Direct Mail Campaign** **Context:** A university wishes to evaluate the cost-effectiveness of its direct mail appeal for contributions from alumni and supporters. Historically, the campaign is deemed too costly if fewer than 16% of the recipients contribute monetarily. An initiative was launched where the director sent out direct mail brochures to a random sample of 321 people from the alumni and supporter mailing lists. This resulted in contributions from 42 individuals. The goal is to determine if this data supports the conclusion that the direct mail campaign is not cost-effective. The analysis is conducted at a 0.05 level of significance. **Step 3 of 3: Conclusion and Interpretation** **Answer Options:** - Option A: We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option B: We reject the null hypothesis and conclude that there is insufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option C: We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. - Option D: We reject the null hypothesis and conclude that there is sufficient evidence at a 0.05 level of significance that the direct mail campaign is not cost-effective. **Explanation:** The task is to decide whether the statistical evidence is strong enough to reject the null hypothesis regarding the campaign's cost-effectiveness. An appropriate choice involves assessing whether the sample contribution rate significantly diverges from the 16% benchmark, using statistical testing methods like the z-test for proportions.
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