imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. each researcher takes a random sample of size 50 from the same population of freshmen. each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 95% confidence interval for the mean. approximately how many of these 100 confidence intervals will not capture the true mean?

Question

Mathematics

Gaven Hamilton

20 January, 11:10

imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. each researcher takes a random sample of size 50 from the same population of freshmen. each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 95% confidence interval for the mean. approximately how many of these 100 confidence intervals will not capture the true mean?

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Answers (1)

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Aspen Gross · Answer 1

Around 5 means 3 to 7 intervals.

Step-by-step explanation:

When we estimate a 95% confidence interval from different samples, we expect 95% of the intervals to include the population mean.

So with 100 different researches, around 95% of 100 (=95) intervals will contain the population mean.

So around (100-95) = 5 intervals will not contain the population mean.

Around 5 means 3 to 7 intervals.

When we estimate a 95% confidence interval from different samples, we expect 95% of the intervals to include the population mean.

So with 100 different researches, around 95% of 100 (=95) intervals will contain the population mean.

So around (100-95) = 5 intervals will not contain the population mean.

Around 5 means 3 to 7 intervals.