A college invited their class of 1992 for a reunion and asked the 50 attendees t

Question

A college invited their class of 1992 for a reunion and asked the 50 attendees their income. The mean of the attendees was $113,217. In a news release, it was announced that "Last year's mean income of members of the class of 1992 was $113,217!"

a.) What assumptions are we making by reporting the mean instead of the median? Do you think it is accurate?

b.) Which method below would you select for estimating the average yearly income of all 6,123 members of the class of 1992? Explain your reasoning and compare the two methods.

(i) Select a simple random sample of members of the class and contact the selected members directly by phone. Follow up to ensure that all responses are obtained. Due to time, it is estimated that 130 members of the class could be contacted.

(ii) Send out an email to all 6,123 members of the class asking them to complete an online form. It is estimated that at least 800 members will respond.

Explanation / Answer

a) Here we are assuming a normal distribution, that is the salary of the sample selected will be distributed about the mean in both directions. This is definitely not going to be accurate because we are then not taking into account the outliers(the extreme values). Salary distributions tend to skew to the right and hence the median would have better measure of the center rather than the mean.

b) Method (i) is better

(i) This method is a simple random sample(SRS) and while the sample size is smaller, it will have a better estimation of the mean, as a random selected sample represents the population. That is, this sample will have more variations of the size of salaries, ranging from small to large.

(ii) This method is based on a voluntary response and hence, we expect that those with higher salaries will be more eager to respond as they have larger salaries. Those with lower or medium salaries may or may not respond and hence the data that we get could be biased and overestimate the actual income.

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