SOLUTION: 6) A local Board of Elections wants to estimate the average number of voters per district for the last election. A random sample of 81 districts shows a sample mean of 168 voters

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Question 983356: 6) A local Board of Elections wants to estimate the average number of voters per district for the last election. A random sample of 81 districts shows a sample mean of 168 voters with a standard deviation of 45 voters. Find a 99% confidence interval (to the nearest tenth) for the population mean number of voters per district.
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Answer by reviewermath(1029) About Me  (Show Source):
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A local Board of Elections wants to estimate the average number of voters per district for the last election. A random sample of 81 districts shows a sample mean of 168 voters with a standard deviation of 45 voters. Find a 99% confidence interval (to the nearest tenth) for the population mean number of voters per district.
Solution:
Central Limit Theorem applies because the sample size, n > 30
R code:
> n = 81
> s = 45
> SE = s/sqrt(n)
> E = qnorm(.995)*SE #margin of error
> xbar =168
> xbar + c(-E, E)
[1] 155.1209 180.8791
The 99% confidence interval for the population mean number of voters per district to the nearest tenth is (155.1, 180.9)
Interpretation:
99% of all samples of size 81 will contain the unknown population mean number of voters per district (μ) between its lower and upper confidence interval limits.