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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