A new process for producing synthetic gems yielded six...

A new process for producing synthetic gems yielded six stones weighting 0,43; 0,52; 0,46; 0,49; 0,60 and 0,56 carats, respectively, in its first run. Find a 90% confidence interval estimate for the mean carat weight from this process. (Assume that the population of carats of all gems produced by this new process is approximately normally distributed.)

Transcript

00:01 All right, so for this problem, we're going to determine the confidence interval at a confidence level of 90%.

00:11 Okay? so in order to solve this problem, we'll be using the formula x bar plus minus, okay, z, s or the standard dev over square root of n.

00:28 Okay.

00:29 Alright, so the first thing to do is of course get the average or the mean which is x bar.

00:44 So to get x bar just have to add everything and then divide the result by how many we have two, four, six, six observations.

00:55 Okay, so you add 0 .43, 0 .52 .46, 0 .49 and 0 .60 and 0 .56 and 0 .56 and 0 .56.

01:07 And divide everything by six, you'll get an average or a sample mean, which is 0 .51.

01:17 Okay? all right.

01:24 So in order to get the standard deviation, you can use calculator a spreadsheet, or you subtract each of the data point to the mean, to the calculated mean, then get the square of it, and then divide it by the number of observations and get the squared of the answer.

01:50 Use the standard deviation, for the sample formula.

01:55 But i did use my calculator and found out that the standard deviation is approximately 0 .063 .2.

02:08 Now, we have to find the value of z.

02:11 Since we have a 90 % confidence level, okay, from the standard normal distribution, we can see that the value of z or from the z table is 1 .645, okay? it's 1 .645 from the z table.

02:36 All right...

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