A large school district would like to estimate the mean score for all of its 5th grade students on a certain mathematics achievement test known to produce scores that are normally distributed in this population.

Question

In a pilot study, n = 25 randomly selected 5th graders take the mathematics achievement test. The sample mean score is 63.4 points and the sample standard deviation is 7.2 points. Construct a 95% confidence interval for the mean score of all 5th graders in the district.
Check conditions
Since the o is unkown we will have to use the t-distribution. Our sample meets the requirements of being a normal population or n≥ 30 and is a random sample.
Critical values
t α/2 = ±2.064
Error
2.064 x 7.2/√25 = 1.44 x 2.064= 2.97216
Margin of error, E= 2.972
standard error= 1.44
Confidence interval
60.428 < μ < 66.372

b:The school board decides to conduct this study again for the next year's class of 5th graders. The school board would like to obtain a 99% confidence interval for the mean score of all 5th graders on the mathematics achievement test with a margin of error on this test of no more than 4 points. How large of a simple random sample should be taken?

How do you solve b?

Answer 1

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