Just as important as calculating a Cl is interpreting it. Below are some reports
ID: 3051387 • Letter: J
Question
Just as important as calculating a Cl is interpreting it. Below are some reports of Cis, each with a number of alternative interpretations or statements. Give your comments on each. As usual, be prepared to use your judgment. 4) We measured subjective well-being on a scale from 1-7 in a sample of participants who had recently won the lottery, and found M4.0, 95% CI [1.5, 6.5). Incidentally, this question is inspired by a fascinating study that actually did measure the happiness of recent lottery winners: (Brickman, Coates, & Janoff-Bulman, 1978). Happiness amongst lottery winners can range from very low to very high. Comments: a. b. In general, lottery winners are likely to be quite happy. Comments: The result is not believable; there must be some flaw in the study. Comments: c. The CI is too long to be interpreted; more data must be collected. Comments: d.Explanation / Answer
(a) This is not correct inerpretation of CI. Confidence interval doesn't provide us the range within which the statistic value will fluctuate. Instead, CI( for eg. 95% CI) tells us that if we repeat the data collection excercise 100 times and make 100 CIs (one in each), 95 of those CIs will contain the actual true value of the parameter inside them. Given CI is one of such 100 CIs.
b. This is also incorrect interpretation of CI. Just because of the fact that mean value of well being score is high in lottery winnner group doesnt guarantee that lottery winners are likely to be happy. For a correct interpretation of CI, please refer to part a.
c. The result is perfectly alright. And there is no flaw in the study either. For a correct interpretation of CI, please refer to part a. of this answer.
d. This is correct interpretation of CI because indeed, the CI interval is almost spanning the entire range of the possible values that the well being score can take. Therefore , such CI is not much informative since they tend to suggest something which we already know.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.