A researcher is interested in the average hours worked in Orange County. She takes a sample...

A researcher is interested in the average hours worked in Orange County. She takes a sample of OC residents (n=81) and finds that the sample mean is 42 hours. The standard deviation is 27.

a. What is the confidence interval around the mean for the 95% confidence level?

b. If the researcher was asked about whether OC residents are on average full-time workers (over 40 hours a week), would this confidence interval help answer that question? Why or why not?

c. A critic claims that because average hours aren't normally distributed, so we can't infer from our sample to the population. Is the critic correct? Why or why not?

Solutions

Expert Solution

a) 95% Confidence interval:

b) Given the statement is the researcher was asked about whether OC residents are on average full-time workers (over 40 hours a week)

This statement is valid since 40 hours is in the above 95% confidence interval.

c) Since the hours are normally distributed the confidence interval of population mean is calculated

from normal distribution if population SD is known or

from t distribution if population SD is unknown.

But if hours are not normally distributed we can not use normal distribution or t distribution for construct the confidence interval then we have to use non parametric confidence interval. In this situation, The claim is may or may not be valid

orchestra answered 1 year ago

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