Mathias was asked whether the following equation is an identity:
2 answers:
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Answer:
a) The standard error would be of 8.58 pounds.
b) The margin of error is 14.11 pounds.
c) The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds
Step-by-step explanation:
a.What is the standard error?
The standard error is
In which is the standard deviation of the population and n is the size of the sample. So
The standard error would be of 8.58 pounds.
b.What is the margin of error at 90% confidence?
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
So it is z with a pvalue of , so
Now, find the margin of error M as such
The margin of error is 14.11 pounds.
c. Using my sample of 30, what would be the 90% confidence interval for the population mean?
Lower bound: Sample mean subtracted by the margin of error.
247 - 14.11 = 232.89 pounds
Upper bound
247 + 14.11 = 261.11 pounds
The 90% confidence interval for the population mean is between 232.89 pounds and 261.11 pounds