In a survey, 100 adults in a certain country were asked how many hours they worked...

In a survey, 100 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: 30 hours and upper bound: 38 hours. Which of the following represents a reasonable interpretation of the result? For those that are not reasonable, explain the flaw. Interpretation #1: There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 30 hours and 38 hours. Flawed. This interpretation implies that the mean is only for last week. 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. 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 30 hours and 38 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 does not make it clear that the 95% is the probability that the mean is within the interval. This is a reasonable interpretation Interpretation #3: 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 30 hours and 38 hours. 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 implies that the population mean varies rather than the interval. Flawed. This interpretation makes an implication about individuals rather than the mean. This is a reasonable interpretation Interpretation #4: 95% of adults in this country worked between 30 hours and 38 hours last week. 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 mean is only for last week. This is a reasonable interpretation

Expert Solution

For the statement:

A 95% confidence interval for mean number of hours worked was lower bound: 30 hours and upper bound: 38 hours.

Interpretation #1: There is a 95% chance the mean number of hours worked by adults in this country in the previous week was between 30 hours and 38 hours.

Flawed. This interpretation implies that the population mean varies rather than the interval.

The population mean has one value. If the experiment is, that true mean wouldn't change. Therefore determining the probability that the population mean lies within a certain range is flawed.

Interpretation #2: We are 95% confident that the mean number of hours worked by adults in this country in the previous week was between 30 hours and 38 hours.

This is a reasonable interpretation

The confidence interval that we compute depends on the data collected. If the experiment is repeated 100 times, each time, the confidence interval would be different. It would be correct if we determine the probability that the interval contains the population mean - We would expect 95% of them (95 out of 100 intervals) to contain the population mean.

Interpretation #3: 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 30 hours and 38 hours.

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.

Interpretation #4: 95% of adults in this country worked between 30 hours and 38 hours last week.

Flawed. This interpretation makes an implication about individuals rather than the mean.

orchestra answered 2 years ago

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