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.

Related questions
See all questions in Confidence Intervals
Impact of this question
9444 views around the world
You can reuse this answer
Creative Commons License