Question

The mayor is interested in finding a 98% confidence interval for the mean number of pounds of trash per person per week that is generated in the city. The study included 237 residents whose mean number of pounds of trash generated per person per week was 37.4 pounds and the standard deviation was 6.1 pounds. Round answers to 3 decimal places where possible.

Answer 1

Solution

Given that,

= 37.4

= 6.1

n = 237

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z _0.01 = 2.326

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

= 2.326 * (6.1 / 237 )

= 0.922

At 98% confidence interval estimate of the population mean is,

- E < < + E

37.4 - 0.922 < < 37.4 + 0.922

36.478 < < 38.322

(36.478, 38.322)