Use the data from 2017 as a sample to estimate the mean...

Use the data from 2017 as a sample to estimate the mean number of home runs hit by a Major League Baseball team each year. There are 30 major league baseball teams so you will have a data set of 30 values. Find a 95% confidence interval for the mean number of home runs hit by a Major League Baseball team each year. Sample Mean = 208.0714, Standard Deviation= 15.55742 128 151 165 168 174 186 186 187 189 192 193 194 196 200 206 212 215 219 220 221 222 223 224 224 228 232 234 237 238 241

Transcript

00:01 All right, so we're looking at the baseball data.

00:04 And the mean attendance per team is normally distributed with a mean of 2 .45 million per team and a standard deviation of 0 .7 .1 million.

00:14 And we're going to get the mean attendance per team for the 2016 season.

00:22 And we're going to determine the likelihood of a sample mean that's this big or larger from the population.

00:30 So that's of all the last decades.

00:33 So let's do that.

00:35 So we've got the mean.

00:39 We're going to compute that the same way we do any mean.

00:42 Let me just go flip, add them up, divide by how many, or just the average function.

00:48 And then we're going to do the standard deviation of the population, which is equal to std -d -p of the data.

01:05 So now, so this is raw attendance.

01:16 So we got to do some configuring here.

01:18 When we do our calculations because this is in this is the the million this is a total this is the sheer number but this we do 2 .4 we have to just remember to do some conversions here when we calculate the z score so we want the z score of this value and i'm just going to round this so we're only dealing with two significant digits 0 .45 so we're going to round this this guy to we're going to say 2 .44 and the sample the standard deviation to point six two because if you notice this is 617 ,000 which is around to 0 .62 million since we're dealing with that level of precision we'll keep that going so we have that so that's the population mean standard deviation oh you know what i made a mistake this would actually be pardon me it's actually going to be the oh geez my face is red i jumped out of myself it's point seven one it's sigma divided by the square root of this of the popular of the sample size which is 30 so total brain fart moment but when you're dealing with a this isn't a population mean this is a sample mean let me correct myself this is a sample or actually this is the standard deviation of the sampling distribution, also known as the standard error.

03:02 So, oof, that was a good little fix.

03:04 I had to correct there.

03:05 So this is 0 .13...

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