Question

For a certain urban area, in a sample of 5 months, an average of 28 mail carriers were bitten by dogs each month. The standard deviation of the population is 3 mail carriers. Find the 90% confidence interval of the true mean number of mail carriers who are bitten by dogs each month.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 28

Population standard deviation =    = 3
Sample size = n =5

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645 ( Using z table )

Margin of error = E = Z_/2    * ( /n)

= 1.645 * (3 /   5)

=2.2
At 90% confidence interval mean
is,

- E < < + E

28 - 2.2 <   < 28+ 2.2

25.8<   < 30.2

(25.8 , 30.2)