Question

You would like to gather data regarding the frequency of headaches. You randomly sample 64 people in the population and find that they suffer an average of 4.5 headaches per month. Suppose the standard deviation of headaches in the population is known to be 2. Calculate the 95% confidence interval for the average number of headaches per month we would expect in the population.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 4.5

Population standard deviation =    =2

Sample size n =64

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* (2 / 64 )

= 0.49
At 95% confidence interval is

- E < < + E

4.5 - 0.49 <   < 4.5+ 0.49

(4.01 , 4.99)