Question

Suppose you gather data from 450 residents in Pullman, Washington about the number of crimes they think happen on a monthly basis in their neighborhood. The answers range from 0 (no crimes) to 50 (this person things 50 crimes happen in Pullman, WA per month). The mean response is 12.3 with a standard deviation of 4.4.

Using this information, construct a 90% confidence interval for the overall mean number of crimes the residents of Pullman think happen. Round all answers to 2 decimal points (0.00). Be sure to interpret your results.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 12.3

Population standard deviation =    = 4.4

Sample size = n =450

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z/2 * ( /n)

= 1.645 * (4.4 /  450 )

= 0.34
At 90% confidence interval estimate of the population mean
is,

- E < < + E

12.3- 0.34 <   <12.3 + 0.34

11.96 <   < 12.64

(11.96 , 12.64)