A direct mail appeal for contributions from a university's alumni and supporters is considered to be too costly if less than 22 % 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 220 people on the alumni and supporters mailing lists. They receive monetary contributions from 37 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. 目 Tables E Keypad Answer Keyboard Shortcuts 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. O 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. 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 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 22 % 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 220 people on the alumni and supporters mailing lists. They receive monetary contributions from 37 people. Does this evidence demonstrate that the direct mail campaign is not cost effective? Use a 0.05 level of significance. Step 3 of 3: Draw a conclusion and interpret the decision. 目 Tables E Keypad Answer Keyboard Shortcuts 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. O 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. 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 at a 0.05 level of significance that the direct mail campaign is not cost effective.
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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
Transcribed Image Text:**Educational Website Content: Understanding Hypothesis Testing in Direct Mail Campaigns**
---
**Context:**
A direct mail appeal targeting contributions from a university’s alumni and supporters is deemed too costly if it garners monetary contributions from less than 22% of the recipients. To assess the cost-effectiveness of this campaign, a fundraising director sent brochures to a random sample of 220 individuals from the alumni and supporters mailing list. The campaign resulted in monetary contributions from 37 people. The objective is to determine if this result provides significant evidence at a 0.05 level of significance that the campaign is not cost-effective.
**Step 3 of 3: Drawing a Conclusion and Interpreting the Decision**
**Analysis and Decision:**
To conclude the hypothesis test, we need to determine which of the following statements is correct based on the evidence and level of significance:
1. **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.
2. **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.
3. **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.
4. **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.
**Explanation:**
Each option involves terms critical to hypothesis testing:
- *Null Hypothesis (H0):* The direct mail campaign is cost-effective.
- *Alternative Hypothesis (H1):* The direct mail campaign is not cost-effective.
- *Level of Significance (α = 0.05):* The threshold for deciding whether to reject the null hypothesis.
**Interpretation Strategy:**
- Rejecting the null hypothesis implies that the evidence supports the campaign being not cost-effective.
- Failing to reject the null hypothesis implies that the evidence is insufficient to deem the campaign not cost-effective.
The analysis must compare the observed proportion (37/220) to the hypothesized proportion (22%) using statistical testing procedures to decide on the correct conclusion based on the evidence provided and the 0.05 significance level.
**Conclusion:**
The final decision should be made based on statistical calculations not shown in this
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