Question

In: Statistics and Probability

A city planner wants to estimate the average monthly residential water usage in the city. He...

A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave the mean water usage to be 3411.10 gallons over a one-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 387.70 gallons. Make a 95% confidence interval for the average monthly residential water usage for all households in this city.

Round your answers to two decimal places.

_____ to_____  gallons

Solutions

Expert Solution

Solution :


Given that,

Point estimate = sample mean = = 3411.10

Population standard deviation =    = 387.70

Sample size n =40

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )


Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 387.70 /  40 )

E= 120.15
At 95% confidence interval estimate of the population mean
is,

- E < < + E

3411.10  - 120.15 <   < 3411.10  + 120.15

3290.95 <   < 3531.25

( 3290.95 , 3531.25 )


Related Solutions

In order to estimate the average electricity usage per month, a sample of 40 residential customers...
In order to estimate the average electricity usage per month, a sample of 40 residential customers were selected, and the monthly electricity usage was determined using the customers' meter readings. Assume a population variance of 12,100kWh2. Use Excel to find the 98% confidence interval for the mean electricity usage in kilowatt hours. Round your answers to two decimal places and use ascending order. Electric Usage 765 1139 714 687 1027 1109 749 799 911 631 975 717 1232 806 637...
In order to estimate the average electricity usage per month, a sample of 125 residential customers...
In order to estimate the average electricity usage per month, a sample of 125 residential customers were selected, and the monthly electricity usage was determined using the customers' meter readings. Assume a population variance of 12,100kWh2. Use Excel to find the 98% confidence interval for the mean electricity usage in kilowatt hours. Round your answers to two decimal places and use ascending order. Electric Usage 765 1139 714 687 1027 1109 749 799 911 631 975 717 1232 806 637...
Python problem Residential and business customers are paying different rates for water usage. Residential customers pay...
Python problem Residential and business customers are paying different rates for water usage. Residential customers pay $0.005 per gallon for the first 6000 gallons. If the usage is more than 6000 gallons, the rate will be $0.007 per gallon after the first 6000 gallons. Business customers pay $0.006 per gallon for the first 8000 gallons. If the usage is more than 8000 gallons, the rate will be $0.008 per gallon after the first 8000 gallons. For example, a residential customer...
A scientist wishes to estimate the average depth of a river. He wants to be 95%...
A scientist wishes to estimate the average depth of a river. He wants to be 95% confident that the estimate is accurate within 3 feet. From a previous study, the standard deviation of the depths measured was 5.48 feet. How large a sample is required? The lifetime of a certain brand of battery is known to have a standard deviation of 23 hours. Suppose that a random sample of 100 such batteries has a mean lifetime of 39.1 hours. Based...
he council wants to construct the facilities that will maximize expected daily usage by the residents...
he council wants to construct the facilities that will maximize expected daily usage by the residents of the community subject to land and cost llimitations. The usage, cost, and land data for each facility are listed below. The community has $240,000 construction budget and 24 arces of land. Because the swimming pool and tennis center must be built on the same part ot the land parcel, however, only one of these two facilities can be constructed. Formulate an optimization mode...
In order to estimate the average electric usage per month, a sample of 47 houses were...
In order to estimate the average electric usage per month, a sample of 47 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 142 kilowatt hours. At 90% confidence, compute the margin of error? In order to estimate the average electric usage per month, a sample of 46 houses were selected and the electric usage determined. The sample mean is 2,000 KWH. Assume a population standard deviation of 127...
A fire insurance company wants to estimate the amount of fire damage in major residential fires...
A fire insurance company wants to estimate the amount of fire damage in major residential fires based on distance between the residence and the nearest fire station. The study is to be conducted in a large suburb of a major city, a sample of 16 recent fires in this suburb is selected. –Explanatory Variable (x): Distance –Response Variable (y): Damage Give a 95% Confidence Interval for slope. (  ,  )
Corporation wants to find an equation to estimate some of their monthly operating costs for the...
Corporation wants to find an equation to estimate some of their monthly operating costs for the operating budget for 2018. The following cost and other data were gathered for 2017​: DATA TABLE : Month Maintenance Costs Machine Hours Health Insurance Number of Employees Shipping Costs Units Shipped January $4,450 158 .    $8,560 58    $22,784      7,120 February $4,375 125 $8,560    79 $26,272 8,210 March $4,675 233    $8,560    91    $25,440 7,950 April $4,880 315    $8,560...
Jordan is developing a business plan for a residential building inspection service he wants to start...
Jordan is developing a business plan for a residential building inspection service he wants to start up. Rent and utilities for an office would cost $1000 per month. The fixed costs for a vehicle would be $450 per month. He estimates that the variable office costs (word processing and supplies) will be $50 per inspection and variable vehicle costs will be $25 per inspection. Jordan would also spend $200 per month to lease a computer, and $350 per month for...
The average monthly electric bill of a random sample of 256 residents of a city is...
The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24. Construct a 95% confidence interval for the mean monthly electric bills of all residents. (Round to two decimal places) [Answer, Answer] Construct a 99% confidence interval for the mean monthly electric bills of all residents. (Round to two decimal places) [Answer, Answer]
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT