11 find each of the following two sided confidence intervals...

11) Find each of the following two-sided confidence intervals for the mean number of pigeons in a flock of those birds if, for a sample of n = 40 flocks, the sample mean number of pigeons is 22.85. Assume $\sigma$ = 4.72. (a) 90% confidence interval (show all work) (b) 95% confidence interval (show all work) (c) 99% confidence interval (show all work)

Transcript

00:01 All right, in your question, you're asked to complete three confidence intervals.

00:04 So a confidence interval is built by taking a statistic plus or minus a critical value times a standard error.

00:11 Your statistic in these questions will be your x bar.

00:15 The critical value is what we typically call z star, and standard error is found by taking the standard deviation of the sample divided by the square to the sample size.

00:26 Now, everything's given to you except for the z star value.

00:30 The z stars are based on your confidence level, and i'm going to show you how we find those.

00:38 Some of these are used so often we should really have them memorized.

00:42 So for example, before i even start here, z star for this question is going to be 1 .645.

00:49 Just because i have that memorized, we use a 90 % confidence interval fairly often.

00:55 But i don't have a 99 % confidence interval memorized.

01:00 So we have to know how to find them.

01:02 You could try to use a z table.

01:05 It's a little bit more challenging, but i'm going to use technology.

01:10 And what a critical value is, it's the upper z score that blocks off the confidence level you want in a normal distribution.

01:21 And the program i use to find those values would be inverse norm, and that can be found on most graphing calculators that have statistical operations or online.

01:33 And what you need to type in first is the area to the left of that z score.

01:38 That's the 90 % and the tail over here to the left, which would be 5%.

01:45 So it's going to be 0 .95 for the first confidence level.

01:52 And then just 0 .1.

01:54 We don't change that.

01:58 So if you type that in your calculator, you should get what i already said.

02:02 The first one's going to be 1 .645, and that is correct.

02:06 Let's do this for all three confidence intervals, and then we'll move on with actually building them.

02:14 So for the 99 % one, if i put a 99 % in here, there's half a percent to the left and half a percent to the right.

02:24 So the area we put in is 0 .99501...

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