In a survey, 1300 adults in a certain country were asked how many hours they wor
ID: 3338161 • Letter: I
Question
In a survey, 1300 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was lower bound: 39.5 and upper bound: 41.3. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw.
(a) There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 39.5
hours and 41.3
hours.
A.
Flawed. This interpretation makes an implication about individuals rather than the mean.
B.
Flawed. This interpretation implies that the mean is only for last week.
C.
Correct
D.
Flawed. This interpretation implies that the population mean varies rather than the interval.
(b) We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between
39.5
hours and
41.3
hours.
A.
Flawed. This interpretation implies that the population mean varies rather than the interval.
B.
Flawed. This interpretation makes an implication about individuals rather than the mean.
C.
Correct
D.
Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.
(c) 95% of adults in this country worked between
39.5
hours and
41.3
hours last week.
A.
Flawed. This interpretation makes an implication about individuals rather than the mean.
B.
Flawed. This interpretation implies that the mean is only for last week.
C.
Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.
D.
Correct
(d) We are 95% confident that the mean number of hours worked by adults in a particular area of this country in the previous week was between 39.5
hours and 41.3
hours.
A.
Flawed. This interpretation makes an implication about individuals rather than the mean.
B.
Correct
C.
Flawed; the interpretation should be about the mean number of hours worked by adults in the whole country, not about adults in the particular area.
D.
Flawed. This interpretation implies that the population mean varies rather than the interval.
Explanation / Answer
a)
Since 95% interval means if we construct many 95% interval for this study then 95% of them will contain true population mean hence
C.
Correct
b)
Since 95% interval means if we construct many 95% interval for this study then 95% of them will contain true population mean hence
A.
Flawed. This interpretation implies that the population mean varies rather than the interval.
c)
Since 95% interval means if we construct many 95% interval for this study then 95% of them will contain true population mean hence
C.
Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.
d)
Since the its confidence interval for whole country hence
C.
Flawed; the interpretation should be about the mean number of hours worked by adults in the whole country, not about adults in the particular area.
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