Question

1. If a random sample of 50 non – smokers have a mean life of 76 years with a standard deviation of 8 years, and a random sample of 65 smokers live 68 years with a standard deviation of 9 years,
   1. What is the point estimate for the difference of the population means?
2. 2. Find a 95% confidence interval for the difference of mean lifetime of non –smokers and smokers.

Answer 1

i)

Point estimate for the difference of the population means = 1 - 2

= 76 - 68

= 8

ii)

= 8.5808

95% Confidence interval is :-
( X̅1 - X̅2 ) ± t( α/2 , n1+n2-2) SP √( (1/n1) + (1/n2))
t(α/2, n1 + n1 - 2) = t( 0.05/2, 50 + 65 - 2) = 1.981
( 76 - 68 ) ± 1.981 * 8.5807 √ ( (1/50) + (1/65))
Lower Limit = ( 76 - 68 ) - 1.981 * 8.5807 √( (1/50) + (1/65))
Lower Limit = 4.8025
Upper Limit = ( 76 - 68 ) + 1.981 * 8.5807 √( (1/50) + (1/65))
Upper Limit = 11.1975
95% Confidence Interval is ( 4.8025 , 11.1975 )