The sugar content of the syrup in canned peaches is normally distributed. a random sample of n = 10 cans yields a sample standard deviation of s = 4.798 milligrams. construct a 95% two-sided confidence interval for σ. round your answers to 2 decimal places.

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

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step-by-step explanation: