A group of 62 randomly selected students have a mean score of 28.3 on a standardized placement test. The population SD for all students taking the test is sigma = 3.4. What is the 90 percent confidence interval for the mean score?

1 Answer
Nallasivam V
Jul 13, 2016

Population mean is likely to fall between 29.005 and 27.595

Explanation:

Given -

barx=28.3
n=62
sigma=3.4
z score for 90% confidence interval 1.64
SE=sigma/sqrtn=3.4/sqrt62=3.4/7.87=0.43

90% confidence interval is defined by the formula

mu=barx+(SExxz) --------upper limit
mu=28.3+(0.43 xx 1.64)=28.3+0.705=29.005

mu=barx-(SExxz) --------Lower limit
mu=28.3-(0.43 xx 1.64)=28.3-0.705=27.595

Look at the diagram

Sample means are normally distributed around the population mean mu

An interval is developed as 29.005 and 27.595. There is 90% chance for the population mean to fall in this interval.

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