Answer:
c
Step-by-step explanation:
Find a 95.0 confidence interval for the population standard deviation σ
A) 2.6194049<σ<6.43192582.6194049<σ<6.4319258
B) 2.2194049<σ<6.83192582.2194049<σ<6.8319258
C) 2.6194049<σ<7.43192582.6194049<σ<7.4319258
D) None of These
Answer:
The confidence interval for the population standard deviation would be:
C) 2.6194049<σ<7.4319258
Step-by-step explanation:
1) Data given and notation
s represent the sample standard deviation
represent the sample mean
n=8 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:
On this case we need to find the sample standard deviation with the following formula:
And in order to find the sample mean we just need to use this formula:
The sample mean obtained on this case is and the deviation s=3.357
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(0.025,7)" "=CHISQ.INV(0.975,7)". 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:
C) 2.6194049<σ<7.4319258