Mathematics, 05.11.2020 21:10 kerriscaballero12

In a survey, 700 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: 35 hours and upper bound: 49 hours. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw.

Interpretation #1: 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 35 hours and 49 hours.
Flawed. This interpretation implies that the population mean varies rather than the interval.
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.
Flawed. This interpretation makes an implication about individuals rather than the mean.
This is a reasonable interpretation

Interpretation #2: We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 35 hours and 49 hours.
Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.
Flawed. This interpretation makes an implication about individuals rather than the mean.
Flawed. This interpretation implies that the population mean varies rather than the interval.
This is a reasonable interpretation

Interpretation #3: There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 35 hours and 49 hours.
Flawed. This interpretation implies that the population mean varies rather than the interval.
Flawed. This interpretation makes an implication about individuals rather than the mean.
Flawed. This interpretation implies that the mean is only for last week.
This is a reasonable interpretation

Interpretation #4: 95% of adults in this country worked between 35 hours and 49 hours last week.
Flawed. This interpretation makes an implication about individuals rather than the mean.
Flawed. This interpretation implies that the mean is only for last week.
Flawed. This interpretation does not make it clear that the 95% is the probability that the mean is within the interval.
This is a reasonable interpretation

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