Question

Prob-3

Breaking strengths of a random sample of 21 molded plastic housing were measured, and a sample standard deviation of S=19.52 was obtained. A confidence interval (439.23, 460.77) for the average strength of molded plastic housings were constructed from these results. What is the confidence level of this confidence interval?

***Provide step-by-step instructions how to solve without skipping steps***

Answer 1

Given data

number of random sample (n)=21

Sample Standard daviation (S)=19.52

Confidence interval =(439.23 , 460.77)

Now we knoe that

where = Sample mean

ME= margional error

Now we have

.....................................(1)

.....................................(2)

Adding both the equation (1)+(2) we have

since we got the Sample mean by puttinng this value in equation (1) we got

we we got the margional error now we have from the formula of margional error

here degree of freedom =N-1=21-1= 20

and = confidencel level

Now from the stanndard T distribution table we have the value of corresponding to the degree of freedom 20 and acd T criticle value 2.528 the criticle region

So the confidence level will be

hence the level of confidence in the given problem is =99%