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To determine how well a new method of teaching vocabulary is working in a certain elementary school, education researchers plan to give a vocabulary test to a sample of 100 sixth graders. It is known that scores on this test have a standard deviation of 8. The researchers found the sample mean to be 100. In order to construct a 95% confidence interval for the population mean, what critical value must be used?

Question
To determine how well a new method of teaching vocabulary is working in a certain elementary school, education researchers plan to give a vocabulary test to a sample of 100 sixth graders. It is known that scores on this test have a standard deviation of 8. The researchers found the sample mean to be 100. In order to construct a 95% confidence interval for the population mean, what critical value must be used?
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Step 1

The critical value for constructing 95% confidence interval is 1.96 and it is calculated below:

The formula for 95% confidence interval for mean is,

х+3,
2
6/45
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х+3, 2 6/45

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Step 2

Here, the critical value is z&...

1-a 0.95
a = 0.05
= 0.025
2
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1-a 0.95 a = 0.05 = 0.025 2

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