Question

A sample of 36 body temperatures body temperatures has a mean of 98.2℉ and a standard deviation of 0.92℉. Construct a 95% confidence interval estimate of the mean body temperature for adults. Interpret your results.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 98.2

Population standard deviation =    =0.92

Sample size n =35

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * ( 0.92 / 35 )

= 0.305
At 95% confidence interval estimate of the population mean
is,

- E < < + E

98.2 - 0.305 <   < 98.2+ 0.305

97.895 <   < 98.505
( 97.895 ,98.505 )