Answer :
In this scenario, we have the average weight of a sample of 20 students in a school, which is found to be 165 lbs, with a standard deviation of 4.5 lbs. We are tasked with constructing a 95% confidence interval for the population mean and determining the margin of error (EBM) for the population mean.
To construct the confidence interval, we can use the formula:
Confidence Interval = Sample Mean ± (Critical Value * Standard Error)
Since the sample size is small (n < 30) and the population standard deviation is unknown, we use a t-distribution and find the critical value associated with a 95% confidence level and degrees of freedom equal to the sample size minus 1. The standard error can be calculated by dividing the sample standard deviation by the square root of the sample size.
Once we have the confidence interval, it represents the range within which we are 95% confident that the true population mean lies.
The margin of error (EBM) is calculated by multiplying the critical value by the standard error. It represents the maximum amount of error we expect to have in estimating the population mean based on the sample.
By calculating the confidence interval and determining the margin of error, we can provide a range estimate for the population mean and understand the precision of our estimate based on the given sample.
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