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A school board wishes to know the current mean reading level of 6th graders throughout a very large school district. Past experience shows that the standard deviation of such reading scores is about 2.5. If they wish to be 95% sure that their result is correct to within .4, how large a sample do they need to have?

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Answer:

Sample size should be atleast 60025

Step-by-step explanation:

Given that a school board wishes to know the current mean reading level of 6th graders throughout a very large school district. Past experience shows that the standard deviation of such reading scores is about 2.5

For 95% confidence we have significance level = 5%

Margin of error = 0.04

Margin of error should be less than 0.04

i.e. Z critical value for 95% *std error <0.04

[tex]1.96*\frac{2.5}{\sqrt{n} } <0.02\\\\n>60025[/tex]

Sample size should be atleast 60025

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