A simple random sample of 90 items resulted in a sample mean...

A simple random sample of 90 items resulted in a sample mean of 80. The population standard deviation is ? = 15. (a) Compute the 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (b) Assume that the same sample mean was obtained from a sample of 180 items. Provide a 95% confidence interval for the population mean. (Round your answers to two decimal places.) to (c) What is the effect of a larger sample size on the interval estimate? A larger sample size provides a smaller margin of error. A larger sample size does not change the margin of error. A larger sample size provides a larger margin of error.

Transcript

00:01 There's a simple random sample of 90 items.

00:03 So there's our sample size, 90.

00:06 And we got a sample mean, x bar, of 80.

00:09 We also know the population standard deviation, sigma.

00:13 It's 15.

00:14 Okay, and we want to make a 95 % confidence interval for the population mean.

00:20 So you need to know the formula for this.

00:23 It's the formula for an interval for the population mean based on a sample mean with a known population standard deviation.

00:31 That formula is x bar plus and minus the margin of error z sigma over root n.

00:39 So we have everything here except z, which we get from a level of confidence.

00:45 So our sample here is a member of a family of samples, every sample of size 90.

00:52 And if you were to take all of these sample means and plot them out, you would get an approximately normal distribution, the sampling distribution.

01:00 We put our sample mean in the middle here, we make an interval around it.

01:05 And we say that 95 % of the area of this curve is in the interval, so we are 95 % confident we have captured the population mean.

01:15 That leaves 5 % in the tails, so each tail is 2 .5%.

01:20 And z is the z score to exclude these tails.

01:27 So sometimes they give you a table of these, but if not, you can need a table of these use the inverse normal function on your graphical calculator or excel or r.

01:35 This is a cumulative function, putting the area to the left, it gives you the critical value.

01:41 So put in 0 .025 or 0 .975, and it gives us z is 1 .960.

01:51 There we go.

01:52 Now we have everything we need to compute the interval.

01:57 So we have 80 plus and minus...

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