Solved on Nov 25, 2023
Estimate the mean water usage in gallons per day for a small town, with a maximum error of 0.15 gallons and 80% confidence. Given that the standard deviation is 2.3 gallons and the mean is 17.6 gallons, determine the required sample size.
STEP 1
Assumptions1. The mean household usage of water is17.6 gallons per day.
. The standard deviation is.3 gallons.
3. The maximum error is0.15 gallons.
4. The level of confidence is80%.
STEP 2
We will use the formula for the sample size in a confidence interval estimation. The formula iswhere- is the sample size- is the Z-score corresponding to the desired level of confidence- is the standard deviation- $$ is the maximum error
STEP 3
First, we need to find the Z-score corresponding to the80% level of confidence. The Z-score for an80% level of confidence is1.28 (you can find this value in a standard Z-table or using a statistical calculator).
STEP 4
Now, plug in the given values into the formula to calculate the sample size.
STEP 5
Calculate the sample size.
STEP 6
Since we can't have a fraction of a sample, we need to round up to the next integer. Therefore, the required sample size is246.
The water works commission needs a sample size of246 to estimate the mean usage of water with a maximum error of0.15 gallons at an80% level of confidence.
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