Department of Mathematics and Statistics QuIZ 4 r 22, 2017 Q1110 Pts] city. He u

Question

Department of Mathematics and Statistics QuIZ 4 r 22, 2017 Q1110 Pts] city. He usage to be 3415.70 gallons over a 1-month period. Based on earlier data, the population standard ]. A city planner wants to estimate the average monthly residential water usage in the selected a random sample of 40 households from the city, which gave the mean water deviation of the monthly residential water usage in this city is 389.60 gallons. a) Find the margin of error with 99% confidence for estimating the average monthly residential water usage for all households in this city. Obtain a 99% confidence interval for the average monthly residential water usage for all households in this city. Interpret your answer. b)

Explanation / Answer

Q.1 Number of housholds surveyed N = 40

Mean water usage of the sample houselholds x = 3415.70 gallons

Sample standard deviation of the water usage for the housholds s= 389.60 gallons

Stanadard error of the sample mean sm  = s/sqrt(n) = 389.60/ sqrt(40) = 61.60 gallons

(a) Margin of error for 99% confidence interval me99= Critical Test statistic * Standard error of the sample mean

= 2.575 * 61.60

= 158.62 gallons

(b) 99% confidence interval for mean water usage for households = x +- me99%

= 3415.70 + 158.62

= (3257.08 gallons , 3574.32 gallons)

(c) Yes, if we reduce the confidence interval from 99% to 95% , critical test statistic will reduce and therefore width of confidence interval will reduce.

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