Question

To estimate mean oil consumption in a population of 10,000 houses. You draw a representative sample of 100 houses from this population. Calculate the mean of the sample (120.6 thermounits) and provide a 95% two-sided confidence interval (118.4 $ µ $ 122.8)... 1- What is the interpretation of this confidence interval?

2- There are several ways to control the width of the confidence intervals. Please name the ways you can change the width of this confidence interval

3- Assume the population is normally distributed, to determine the variance of this population

Answer #1

1. The population mean oil consumption in a population of 10,000 houses will lie in the range of 118.4 to 122.8

2. Width of the confidence interval depends on sample size, as we increase in sample size it will decrease the width, as increasing sample size, standard error will decrease. Confidence level also effects the width, increasing confidence level will increase the width. Standard deviation can also change the width, increasing standard deviation will increase the width of CI

For this term, we will create confidence intervals to estimate a
population value using the general formula:
sample estimator +/- (reliability factor)(standard error
of the estimator)
Recall that the (reliability factor) x (standard error of the
estimator)= margin of error (ME) for the interval.
The ME is a measure of the uncertainty in our estimate of the
population parameter. A confidence interval has a width=2ME.
A 95% confidence interval for the unobserved population
mean(µ), has a confidence level =
1-α...

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