How to establish a 95% and 97.5% confidence interval for the average heights of the female and male students? How to do the same for the students population regardless of the Gender. How to compare?
1 Answer
Refer explanation section
Explanation:
Limitation
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The Solution.
Formula for Interval Estimate -
#mu=barx+-(zxxS.E)#
Where -
#mu=# Population mean
#barx=# Sample mean
#z=( )# Table Value or critical value for a given confidence level.
#S. E=sigma/sqrtn# Standard Error.
You find two limits
Upper limit is given by
Lower limit is given by
Population mean is expected to fall between
#z=1.96# for 95% confidence level
#z=2.24 # for 97.5% confidence
Female
Mean
S.D
SE
95% confidence interval estimate
Upper Limit
#mu=162.24+(1.96 xx 1.14) #
#mu=162.24+2.23 #
#mu=164.47#
Lower Limt
#mu=162.24-(1.96 xx 1.14) #
#mu=162.24-2.23 #
#mu=160.01#
We are 95% confident that female height falls between 160.01 and 164.47
97.5% confidence interval estimate
Upper Limit
#mu=162.24+(2.24 xx 1.14) #
#mu=162.24+2.55 #
#mu=164.79#
Lower Limit
#mu=162.24-(2.24 xx 1.14) #
#mu=162.24-2.55#
#mu=159.69#
We are 97.5% confident that female height falls between 159.69 and 164.79.
Male
Mean
S.D
SE
95% confidence interval estimate
Upper Limit
#mu=175.39+(1.96 xx 0.91) #
#mu=175.39+1.78 #
#mu=177.17#
Lower Limt
#mu=175.39-(1.96 xx 0.91) #
#mu=175.39-1.78 #
#mu=173.61#
We are 95% confident that female height falls between 173.61 and 177.17
97.5% confidence interval estimate
Upper Limit
#mu=175.39+(2.24 xx 0.91) #
#mu=175.39+2.03 #
#mu=177.42#
Lower Limit
#mu=175.39-(2.24 xx 0.91) #
#mu=175.39-2.03#
#mu=173.36#
We are 97.5% confident that female height falls between 173.36 and 177.42.
Population
Mean
S.D
SE
95% confidence interval estimate
Upper Limit
#mu=168.81+(1.96 xx 1.03) #
#mu=168.81+2.02 #
#mu=170.83#
Lower Limt
#mu=168.81-(1.96 xx 1.03) #
#mu=168.81-2.02 #
#mu=166.79#
We are 95% confident that female height falls between 166.79 and 170.83
97.5% confidence interval estimate
Upper Limit
#mu=168.81+(2.24 xx 1.03) #
#mu=168.81+2.3 #
#mu=171.11#
Lower Limit
#mu=168.81-(2.24 xx 1.03) #
#mu=168.81-2.3#
#mu=166.51#
We are 97.5% confident that female height falls between 166.51 and 171.11.
