From: Siegel, A.F. (1997). Practical Business Statistics, 3rd Edition. Irwin/McGrawHill.
Case - Can This Survey Be Saved?
"What's troubling me is that you can't just pick a new random sample just because somebody didn't like the results of the first survey. Please tell me more about what's been done." Your voice is clear and steady, trying to discover what actually happened and, hopefully, to identify some useful information without the additional expense of a new survey.
"It's not that we didn't like the results of the first survey," responded Steegmans, "it's that only 54% of the membership responded. We hadn't even looked at their planned spending when the decision [to sample again] was made. Since we had (naively) planned on receiving answers from nearly all of the 400 people initially selected, we chose 200 more at random and surveyed them also. That's the second sample." At this point, sensing that there's more to the story, you simply respond "Uh huh . . ." Sure enough, more follows: "Then Eldredge had this great idea of following up on those who didn't respond. We sent them another whole questionnaire, together with a crisp dollar and a letter telling them how important their responses are to the planning of the industry. Worked pretty well. Then, of course, we had to follow up the second sample as well."
"Let me see if I understand," you reply. "You have two samples: one of 400 people and one of 200. For each, you have the initial responses and followup responses. Is that it?"
"Well, yes, but there was also the pilot study - 12 people in offices downstairs and across the street. We'd like to include them with the rest because we worked so hard on that at the start, and it seems a shame to throw them away. But all we really want is to know average spending to within about a hundred dollars."
At this point, you feel that you have enough of the background information to evaluate the situation and to either recommend an estimate or an additional survey. Additional details for the survey of the 8,391 overall membership in order to determine planned spending over the next quarter are provided on the following page.
Discussion Questions
1.Do you agree that drawing a second sample was a good idea?
2.Do you agree that the followup mailings were a good idea?
3.How might you explain differences among averages in the results?
4.Are there useful results here? Which ones are useful? Are they sufficient, or is further study needed?
Pilot
Study First Sample Second Sample Both Samples All Combined
Initial Mailing
Mailed 12 400 200 600 612
Responses 12 216 120 336 348
Average $39,274.89 $3,949.40 $3,795.55 $3,894.45 $5,114.47
Std. Dev. $9,061.91 $849.26 $868.39 $858.02 $6,716.42
Followup Mailing
Mailed 0 184 80 264 264
Responses 0 64 18 82 82
Average $1,238.34 $1,262.34 $1,243.60 $1,243.60
Std. Dev. $153.19 $156.59 $153.29 $153.29
Initial and Followup Mailings Combined
Mailed 12 400 200 600 612
Responses 12 280 138 418 430
Average $39,274.89 $3,329.73 $3,465.13 $3,374.43 $4,376.30
Std. Dev. $9,061.91 $1,364.45 $1,179.50 $1,306.42 $6,229.77
To answer the questions, we need to analyze the given data. Let's start by understanding the information provided.
From the information given, we can see that the survey was conducted using multiple samples: the pilot study, the first sample, and the second sample. Each sample had an initial mailing and a follow-up mailing. The number of mailed surveys and the number of responses are provided for each sample.
Now let's examine each question to provide an answer and explanation:
1. Do you agree that drawing a second sample was a good idea?
To assess whether drawing a second sample was a good idea, we need to consider why it was done in the first place. According to the information provided, the decision to sample again was made because only 54% of the membership responded to the first survey. However, this decision was made before looking at the planned spending data. Without knowing the initial results, it is difficult to determine whether a second sample was necessary. Therefore, the answer to this question is subjective and dependent on the initial survey results.
2. Do you agree that the follow-up mailings were a good idea?
The follow-up mailings were done to increase the response rate of the surveys. It seems that they were somewhat effective since additional responses were obtained. However, it is important to note that the number of responses from the follow-up mailings was smaller compared to the initial mailings. Whether the follow-up mailings were a good idea or not depends on the resources and time invested in creating and sending the additional questionnaires, as well as the significance of the gained responses.
3. How might you explain differences among averages in the results?
To explain differences among averages in the results, we need to compare the averages of the different samples. From the data provided, we can see that the average spending differs across the pilot study, first sample, second sample, and the overall combination of all samples. These differences could be due to various factors, such as the characteristics of the samples, response rate, respondent demographics, or other variables not mentioned in the case study. Without more information, it is challenging to pinpoint the exact reasons for the differences. Further analysis and investigation would be required to provide a more accurate explanation.
4. Are there useful results here? Which ones are useful? Are they sufficient, or is further study needed?
There are useful results present in the data. The usefulness of the results depends on the specific objectives of the survey. In this case, the objective is to determine average spending within a hundred dollars. From the data, we can see the average spending values for each sample. However, since the standard deviation values are relatively high, it suggests that there is a significant amount of variability in the data. To determine if further study is needed, we need to consider the desired level of precision and the cost-benefit trade-off of conducting another survey. If a smaller standard deviation is desired, further study may be needed to reduce the variability in the results.
Overall, a more comprehensive analysis of the data, including additional statistical methods, would be necessary to draw concrete conclusions and make recommendations.