An airplane manufacturer needs to purchase an aluminum alloy for use in constructing a part for their new line of jumbo jets. It
1 answer:
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Answer:
a)
b) The margin of error indicates we can be 95%confident that the sample mean falls within 0.89 of the population mean
Step-by-step explanation:
Part a
The best point of estimate for the population mean is the sample mean given by:
Since is an unbiased estimator
Data given: 2 , 2 , 1 , 3 , 1 , 0 , 4 , 1
So for this case the sample mean would be:
Part b
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean for the sample
population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
The confidence interval for the mean is given by the following formula:
(1)
The margin of error is given by this formula:
(2)
And for this case we know that ME =0.89 with a confidence of 95%
So then the limits for our confidence level are:
So then the best answer for this case would be:
The margin of error indicates we can be 95%confident that the sample mean falls within 0.89 of the population mean