Question

estimate monthly water useage. a random sample of 100 is selected, which gave a mean water usage of 4000 gal over 1 month. standard deviation is 450 gal. make 99% confidence interval for the avegage montjly resudential water usage for all house holds.

1) give a point estimate for the average mothly residental water useage for all hosue holds.

2) construct a 99% confidnece interval for the average monthly residnetial water useage for all households.

3) conduct a new study. what samplw size is required if you want to be 99% sure that the true mean is estimated within 100 gal

Answer 1

solution :

Given that n = 100 , mean x = 4000 , standard deviation σ = 450

1)
=> Point estimate of the mean x = 4000

2)
=> for 99% confidence interval, Z = 2.58

=> A 99% confidence interval of the mean is

=> x +/- Z*σ/sqrt(n)

=> 4000 +/- 2.58*450/sqrt(100)

=> (3883.9 , 4116.1)

3)
=> given that margin of error E = 100

=> for 99% confidence interval, Z = 2.58

=> Sample size n = (Z*σ/E)^2

= (2.58*450/100)^2

= 134.7921

= 135 (nearest whole integer)