Question

A random sample of 20 houses selected from a city showed that the mean size of these houses is 1880 square feet with a standard deviation of 320 square feet. Assume that the sizes of all houses in this city have an approximate normal distribution. The upper bound the 90% confidence interval for the mean size of all houses in this city is: A. 2110 B. 1941 C. 1974 D. 1968 E. 1894

Answer 1

Option C

Explanation:

Given that for a random sample of 20 houses selected from a city showed that the mean size of these houses is 1880 square feet with a standard deviation of 320 square feet.

X, the sizes of houses is Normal

Hence sample mean will be normal with

Mean = 1880

and std dev =
`(320)/(√(20) ) \\=71.5542`

For 90% confidence interval critical value for t with degree of freedom 19 is

1.328

Confidence interval upper bound

= mean + margin of error

=
`1880+1.328*71.55\\=1975`

Option C is right