One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.

Question

Mathematics

Harrington

26 August, 07:57

One researcher wishes to estimate the mean number of hours that high school students spend watching tv on a weekday. a margin of error of 0.23 hour is desired. past studies suggest that a population standard deviation of 1.9 hours is reasonable. estimate the minimum sample size required to estimate the population mean with the stated accuracy.

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Ariella Burton · Answer 1

Margin of error, e = Z*SD/Sqrt (N), where N = Sample population

Assuming a 95% confidence interval and substituting all the values;

At 95% confidence, Z = 1.96

Therefore,

0.23 = 1.96*1.9/Sqrt (N)

Sqrt (N) = 1.96*1.9/0.23

N = (1.96*1.9/0.23) ^2 = 262.16 ≈ 263

Minimum sample size required is 263 students.