Question

A sample of 50 cotton threads shows the mean breaking strength to be 220 grams and the sample standard deviation to be 12 grams. What is the 95% confidence interval for the standard deviation of breaking strength of the thread.

Answer 1

`220-2.01(12)/(√(50))=216.589`

`220+2.01(12)/(√(50))=223.411`

The confidence interval for this case would be (216.589, 223.411)

Explanation:

Information given

`\bar X=220` represent the sample mean

`\mu` population mean

s=12 represent the sample standard deviation

n=50 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

The degrees of freedom are given by:

`df=n-1=50-1=49`

The Confidence level is 0.95 or 95%, the significance is
`\alpha=0.05` and
`\alpha/2 =0.025`, the critical value for this case is
`t_(\alpha/2)=2.01`

And replacing we got:

`220-2.01(12)/(√(50))=216.589`

`220+2.01(12)/(√(50))=223.411`

The confidence interval for this case would be (216.589, 223.411)