To help in the solicitation of contributions, a foundation considered hiring a c
ID: 3222944 • Letter: T
Question
To help in the solicitation of contributions, a foundation considered hiring a consulting firm. The firm claimed that the mean contribution from families who contribute after receiving a specially prepared letter would be $21.00. Before hiring the firm, the foundation sent out the letter and request materials. They received the 30 contributions shown below. Complete parts a and b.
13.00 28.00 2.00 7.00 39.00 16.00 21.00 19.00 19.00 8.00 15.00 13.00 21.00 30.00 33.00
37.00 12.00 28.00 12.00 8.00 3.00 32.00 9.00 7.00 19.00 8.00 29.00 22.00 8.00 11.00
a. Assuming that these data reflect a random sample of the population of contributions that would be received, compute the sampling error based on the claim made by the consulting firm.
The sampling error based on the claim made by the consulting firm is $ ___ (Round to two decimal places as needed.)
b. Are there any issues with the assumption that the data represent a random sample? Does the calculation of the sampling error matter if the sample is not a random sample?
A. There is no indication that the sample is random. Since the sample is not random, the calculation of the sampling error is not valid. A random sample must be obtained in order to calculate an accurate sampling error.
B. The calculation of the sampling error does not depend on whether the sample is random, so the sampling error can be used to determine if the sample is random. Since the sampling error is small, it appears that the sample is random.
C. The sample may be random, but there is no way to be certain because we have no knowledge of the sample or how it was obtained. However, the calculation of the sampling error does not depend on whether the sample is random.
Explanation / Answer
a) From the given data,
Descriptive Statistics: Sample
Sum of
Variable CumN Mean SE Mean StDev Variance Sum Squares
Sample 30 17.63 1.89 10.35 107.21 529.00 12437.00
Sample Mean = 17.63 and Popution Mean = 21
Sampling error = 21 - 17.63 = 3.37
b) Correct Answer:
C. The sample may be random, but there is no way to be certain because we have no knowledge of the sample or how it was obtained. However, the calculation of the sampling error does not depend on whether the sample is random.
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