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Chapter 6: Problem 93

A sample with \(n=75, \bar{x}=18.92,\) and \(s=10.1\)

Short Answer

Expert verified
To find the 95% confidence interval for the mean, first calculate the standard error by dividing the standard deviation by the square root of the sample size. Then find the critical value for a 95% confidence interval from the Z-table. Finally, multiply the standard error by the critical value and subtract and add this to the mean to get the confidence interval.

Step by step solution

01

Calculate Standard Error

First, calculate the standard error of the sample mean by dividing the standard deviation by the square root of the sample size.\[SE = \frac{s}{\sqrt{n}} = \frac{10.1}{\sqrt{75}}\]
02

Determine the Z-score

Under normal circumstances, and considering a 95% confidence interval, the z-score (critical value) we would use is 1.96. Verify this value from the standard normal distribution table for a 95% confidence interval.
03

Calculate Confidence Interval

Finally, the confidence interval is calculated by multiplying the standard error by the Z-score and adding/subtracting that value from the sample mean. Express this in the format (\( \bar{x} - Z*SE, \bar{x} + Z*SE \))

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Most popular questions from this chapter

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