Answer to Question #102345 in Statistics and Probability for Mohammad Islam

Question

A sample of 100 apparently normal males, 25 years old, had a mean systolic blood pressure 125.It is believed that the population standard deviation is 15.
a) Construct a 97 % confidence interval for the mean systolic blood pressure of adult males.
b) How many adult males must we select so that the margin of error is not greater than 2.5 considering the confidence level of 98 % ?

Answer 1

a) Construct a 97% confidence interval.

n=100, x ̅= 125,,σ=15

1-α=0.97, α=0.03, α/2=0.015, 1-0.015=0.985,

The value of 98.5 percentile from the table is 2.17

Confidence interval is within x ̅±E ; where E= (z_(α/2)* σ)/√n

E= (2.17*15)/√100=3.255

(125-3.255, 125+3.255)

Ans

=(121.745, 128.255)

b) Number of males to be selected so that E is not greater than 2.5 at 98% confidence interval

n=((z_(α/2)* σ)/E)^2; where E=margin error

1- α=0.98, α=0.02, α/2=0.01, 1-0.01=0.99

The value of the 99 percentile from the table is 2.33

n = ((2.33*15)/2.5)^2=13.98²=195.44

Ans

=Approximately 196 adult males