Question

A random sample of body temperatures of 100 healthy American adult males has a sample mean of 97.78◦F and a sample standard deviation of 1.2◦F. Which of the following is the correct 95% confidence interval for the true mean body temperature for all American adult males.

97.78◦F ± 1.2◦F

97.78◦F ± 0.24◦F

97.78◦F ± 0.12◦F

97.78◦F ± 2.4◦F

Answer 1

Solution :

Given that,

= 97.78

s =1.2

n =100

Degrees of freedom = df = n - 1 = 100 - 1 = 99

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,99 = 1.984 ( using student t table)

Margin of error = E = t/2,df * (s /n)

=1.984 * (1.2 / 100)

= 0.24

The 95% confidence interval estimate of the population mean is,

- +E

97.78◦F ± 0.24◦F