Paige is a graphic designer who makes logos for companies. She makes a design for a logo, which is in the shape of a square. The
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Answer:
The 95% confidence interval is given by:
3.30<σ<8.76
Step-by-step explanation:
1) Data given and notation
s=4.798 represent the sample standard deviation
represent the sample mean
n=10 the sample size
Confidence=95% or 0.95
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 mean or variance 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.
The Chi Square distribution is the distribution of the sum of squared standard normal deviates .
2) Calculating the confidence interval
The confidence interval for the population variance is given by the following formula:
The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a tabel to find the critical values.
The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:
And replacing into the formula for the interval we got:
Now we just take square root on both sides of the interval and we got:
So the best option would be:
3.30<σ<8.76