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Answer:
And the best conclusion would be:
D. This conclusion is safe because 1.40 °F is outside the confidence interval.
Step-by-step explanation:
1) Data given and notation
s=0.68 represent the sample standard deviation
represent the sample mean
n=98 the sample size
Confidence=90% or 0.90
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 0.90 or 90%, the value of and
, and we can use excel, a calculator or a table to find the critical values.
The excel commands would be: "=CHISQ.INV(0.05,97)" "=CHISQ.INV(0.95,97)". 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:
And the best conclusion would be:
D. This conclusion is safe because 1.40 °F is outside the confidence interval.