SOLUTION: A well-known consulting firm wants to test how it can influence the proportion of questionnaires returns for its surveys. In the belief that the inclusion of an inducement to respo

Question 1177326: A well-known consulting firm wants to test how it can influence the proportion of questionnaires returns for its surveys. In the belief that the inclusion of an inducement to respond may be influential, the firm sends out 1000 questioners: 200 promise to send respondents a summary of the survey results; 300 indicate that 20 respondents (selected by a lottery) will be awarded gifts; and 500 are accompanied by no inducements. Of these, 80 questionnaires promising a summary, 100 questionnaires offering gifts, and 120 questionnaires offering no inducements are returned. What can you conclude from these results?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Let's analyze the questionnaire return rates for each group to draw conclusions about the effectiveness of inducements.
**1. Calculate Return Rates for Each Group**
* **Summary Group:**
* Number sent: 200
* Number returned: 80
* Return rate: (80 / 200) * 100% = 40%
* **Gift Group:**
* Number sent: 300
* Number returned: 100
* Return rate: (100 / 300) * 100% = 33.33%
* **No Inducement Group:**
* Number sent: 500
* Number returned: 120
* Return rate: (120 / 500) * 100% = 24%
**2. Compare Return Rates**
* The summary group had the highest return rate (40%).
* The gift group had a return rate of 33.33%.
* The no inducement group had the lowest return rate (24%).
**3. Draw Preliminary Conclusions**
* Offering a summary of the survey results appears to be the most effective inducement in increasing questionnaire returns.
* Offering a lottery for gifts also increased returns compared to no inducement, but was less effective than offering a summary.
* Offering no inducements resulted in the lowest return rate, as expected.
**4. Statistical Significance (Considerations)**
While the return rates show a clear trend, it's important to consider statistical significance. To be more certain of the conclusions, the consulting firm should perform a statistical test, such as a chi-square test or a proportion test, to determine if the differences in return rates are statistically significant.
**5. Potential Factors**
* **Perceived Value:** The perceived value of a survey summary might be higher than the perceived value of a lottery gift, especially for professionals.
* **Effort:** The effort needed to recieve the summary is less than the effort needed to win the gift lottery.
* **Trust:** People may trust the summary more than the lottery.
* **Sample Size:** Although the sample size is relatively large, a larger sample size would yield more accurate results.
**Conclusion**
Based on the observed return rates, the consulting firm can conclude that offering a summary of survey results is the most effective inducement to increase questionnaire returns. Offering a lottery for gifts is also effective, but less so. Offering no inducements results in the lowest return rate. However, to confirm these conclusions and establish statistical significance, further statistical testing is recommended.

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