Confidence Interval

Question

The amount of trash generated by US households (in lbs per day) is Normally distributed. You a random sample of 8 people gives you an average of 10.00 lbs and a sample stdev of 5 lbs. What is the 90% Conf. Int. for the mean?

Group of answer choices

8.36 to 11.64

6.65 to 13.35

8.59 to 11.41

8.14 to 11.86

Answer 1

CI = x bar +/-z(s)/sqrn, n=sample size,s=population standard deviation when n<30 z= z score for 90%

x bar = mean. find z from z tables or a z calculator. You know it's less than 2 from the empirical rule, as 95% has a z score =2. For 90% z=1.64. sqr8 is slightly less than 3, since sqr9=3

population standard deviation = sample standard deviation times sqr(n) = 5sqr8

CI = 10+/-z(pop s)sqrn

CI= 10+/- 1.64(5sqr8)/sqr8

=10+/- 1.64(5)

= 10+/-8.2

= (1.8, 18.2)

closest is 2nd choice

if you use the sample standard deviation, then

CI= 10+/-1.64(5)/sqr8

= about 10+2.9 and 10-2.9

= (7.1, 12.9)

2nd choice is closest again= "best answer"

on most tests, they say choose "best" answer, if none are correct

it's also possible the problem was misprinted or miscopied

when none of the answer options are close to correct

Margin of Error, MOE for the 4 options are

1.64

3.35

1.41

1.86

CI = xbar+/-MOE= 10+/-MOE

MOE= zs/sqrn = 1.64s/sqr8

option 1 suspiciously uses the z score, so you could be nearly certain it's incorrect

option 3 is just too small for MOE

option 2 and 4 are odds on favorites with 2 closer

5/sqr8 = about 1.77