Question

2) Suppose we want to estimate the mean mortage layment for homes in Denver. Suppose that it is known from past data thag the mean monthly mortage payment is $2500 with a standard deviation of $1000. If we want to be 92% confident that lur sample mean is within $300 of the population mean, what is the recommended sample size?

3) Suppose we want to estimate the proportion of homes in Denver that are valued at over $1,000,000. Suppose that it is known from past data that the proprotion of such homes in Denver is 15%. If we want to be 82% confident that our sample proportion is within 4% of the population proportion, what is the recommended sample size?

please write it out..

Answer 1

2)

Given that,

Population standard deviation = = 1000

Margin of error = E = 300

Z_/2 = 1.75

sample size = n = [Z_/2* / E] ²

n = [1.75 * 1000 / 300]²

n = 34.02

Sample size = n = 35

3)

Given that,

= 0.15

1 - = 0.85

margin of error = E = 0.04

Z_/2 = 1.34

sample size = n = (Z _{/ 2} / E)² * * (1 - )

= (1.34 / 0.04)² * 0.15 * 0.85

= 143.08

sample size = n = 144