A sample standard deviation of 10 weights of packages of grass seed distributed by a certain company was calculated to be 0.286. Assume that weights are normally distributed and find a 95% confidence interval for the standard deviation of all such packages of grass seed

Now we just take square root on both sides of the interval and we got:

Step-by-step explanation:

Data given and notation

s=0.286 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 .

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 table 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:

step-by-step explanation: