A sample of 23 observations is selected from a normal population. The sample standard deviation is 23.25, and the sample mean is 54.

The standard error of the mean is 

The 80% confidence interval for the population mean is between

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Standard error of the mean=23.25/√23=4.85 approx.

To find the Z value for 80%, 1-0.80=0.20, halve this: 0.10 and subtract from 1=0.9, so we look in the body of the normal distribution table for closest value of Z, and Z=1.282. This is applied to the standard error to give the margin on the mean.

80% confidence interval for the population mean is 54±1.282×4.85=54±6.2 or between 47.8 and 60.2 approx.

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