Qs. 6 A civil engineer is analyzing the compressive strength...

Qs. 6 A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with ?^2 = 1000 (psi)^2. A random sample of 12 specimens has a mean compressive strength of x? = 3250 psi. [15 points] (a) Construct a 99% two-sided confidence interval on mean compressive strength. (b) Construct a 95% two-sided confidence interval on mean compressive strength. Compare the width of this confidence interval with the width of the one found in part (a). (c) Suppose that it is desired to estimate the compressive strength with an error that is less than 15 psi at 95% confidence. What sample size is required?

Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:08 In this question we want to discuss about the company interval for the mean.

00:12 Now let me remind you that the company interval for the mean with the sigma is unknown.

00:24 It will be x bar plus or minus t degree of freedom equal to n minus 1 and 5 over 2.

00:32 Time with the s over square at n.

00:36 In this question here we're given the sigma square it will equal to the 100 1000 and then we're given the sample on the end equal to the 12 and the x bar equal to the 3 -250.

00:57 Now notice that we're given the true population standard deviation therefore we will use another formula for the is known and then we have the xb plus or minus z alpha over 2 time with the sigma over square and therefore in the question a we want to find the 99 % complete interval so first of all we have to use this formula because the sigma is known and then the next step we need to find the z alpha over 2 now because of the 99 % so n5 equal to 1%.

01:39 Therefore the nphal of 2 it will equal to the 0 .5 % or it will equal to the 0 .05.

01:51 And then we have to define the z of the 0 .005.

01:55 Then we look at the z table.

01:58 The file will correspond to the 2 .575.

02:02 Therefore we will have the 99 % cost.

02:07 The interval for the mean it will be x -par will be the 3250 plus and minus zan 5 over 2 .575 times the s sigma will be square root of the 1 ,000 divided by square root to the n will be the 12 it will compute the value we will have plus and minus here we have the 1 ,000 divided by 2nd taking the square root 1020 .575 equal to the 23 .506.

02:48 And if we use the minus, we should get the 3250 minus that equal to the 326 .49.

03:02 And if we use the plus, we will have equal to the 325.

03:12 273 .5 .06 and that will be the 99 % comfortable for the part a.

03:21 For the part b we need to constrict the 95%.

03:24 So 95 % means that unfine equal to the 5%.

03:29 So nfile over 2 equal to the 2 .5%, which is equal to the 0 .025...

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