A random sample of 10 children found that their average growth for the first year was 9.8 inches. What is the 95% confidence interval of the population mean for growth during the first year?

Assume the variable is normally distributed and the sample standard deviation is 0.96 inch.

1 Answer
Nallasivam V
Sep 19, 2016

95% of the confidence interval between #10.48#and #9.12#

Explanation:

Sample size #n=10#
Sample Mean #barx=9.8# inches
Sample SD #=0.96# # # inch
Confidence Interval 95%

The solution -

#mu=barx+- t*SE#

Where -

#mu -> #Population Mean

#t-># Critical Value - for 95% confidence and 9 degrees of freedom #2.262#

#SE-># Standard error

#SE=s/sqrtn=0.96/sqrt10=0.96/3.16=0.3#

#mu=9.8+-(2.262xx0.3)#

Upper limit

#mu=9.8+0.68=10.48#

Lower limit

#mu=9.8-0.68=9.12#

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