A laboratory tested 42 chicken eggs and found that the mean...

Name: a laboratory tested 42 chicken eggs and found that the mean amount of cholesterol was 239 milligrams with a standard deviation of 133 milligrams construct a 99 confidence interval for the me 91564
Uploaded: 2022-04-17T23:08:31-08:00
Duration: 6 min 47 s
Channel: Jon Southam
Description: a laboratory tested 42 chicken eggs and found that the mean amount of cholesterol was 239 milligrams with a standard deviation of 133 milligrams construct a 99 confidence interval for the me 91564

A laboratory tested 42 chicken eggs and found that the mean amount of cholesterol was 239 milligrams with a standard deviation of 13.3 milligrams. Construct a 99% confidence interval for the mean cholesterol contents of all such List the path you will take to solve this problem. List the sample data you are using. Identify the lower and upper limits (round to one decimal place) Write the appropriate confidence interval sentence.

Transcript

00:01 All right, so we have a nice little confidence interval exercise here.

00:06 I've got laboratory chicks, chicken eggs, and the mean amount of cholesterol, and that's what we're looking at.

00:17 So the point estimate for the mean amount of cholesterol is 193 milligrams.

00:27 And then just so we're clear, we have the stand sample standard deviation of 12.

00:33 And then what we want to do is, oh, check the requirements for our confidence interval.

00:36 Well, first off, we have to, we're assuming the population is normal.

00:42 We don't really know much about it.

00:44 But because we have an n greater than 30, see how it's 32, then we can apply the central limit theorem, which basically says that regardless of the distribution, if you have a sample size greater than 30, we can, the distribution will be approximately normal.

01:05 So it's good.

01:06 And we also have to have simple range.

01:09 Samples, just the idea of independent sampling.

01:15 So we're good.

01:17 So sample size and then central limit theorem.

01:22 Those are two big, big things we have to know, central limit theorem.

01:28 So now we can do our confidence interval, and we're going to use the t distribution, the t, use our t tables because we don't know the population standard deviation.

01:40 So we have to use the t distribution at this point.

01:43 That's fine.

01:43 We can do that.

01:44 And remember, we're approximately normal, so it's all good.

01:48 So for 90 % confidence interval, oh, let's do our formula first.

01:52 It's t.

01:53 Whoops, sorry, no.

01:54 It's a t -dist confidence interval.

02:02 It's going to be x bar, the point estimate, plus or minus our t, the alpha over two, comma, degrees of freedom, times this, times the sample, standard deviation over root n.

02:19 So here let's do our 90 % interval, 90 % confidence interval.

02:26 Let's get our t value.

02:28 It's alpha of 0 .1 over 2, with degrees of freedom of 31, and that is 1 .6.

02:41 And while we're at, we'll just keep going.

02:45 The 95 % has a t value of 0 .05 over 2.

02:53 Degrees of freedom of 31 and that is 2 .04 and then 99 % confidence interval with the t .1 over 2 degrees of freedom 31 is 2 .744.

03:12 So we just plug in our values and we get our interval so let's do this first one for 90%.

03:19 The x is 193 plus or minus the t value at 1 .696 times a the standard deviation of 12 over root 32.

03:34 And then what we're gonna get is a confidence interval.

03:40 It goes from 189 .40 to 196...

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