You are interested in finding a 90 confidence interval for...

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 12 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. 14 23 10 21 21 23 24 25 24 28 5 22 a. To compute the confidence interval use a ? z t distribution. b. With 90% confidence the population mean number of visits per physical therapy patient is between_______ and______ visits. c. If many groups of 12 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About_________ percent of these confidence intervals will contain the true population mean number of visits per patient and about_________ percent will not contain the true population mean number of visits per patient.

Transcript

00:01 Okay, so we're trying to find a 90 % comments interval for the main number of visits for physical therapy patients, and we have data on these tall visits, and we're going to compute the comments interval using this formula.

00:19 So we're going to use the formula x bar plus and minus our t star, there's our critical value, times the standard deviation of our sample.

00:30 Divided by the square root of our sample.

00:35 Okay, so for this, you're going to want to, you know, enter your data into your calculator.

00:43 So your calculator, go to stats.

00:46 If you're not familiar with it, i'll, i'll, you know, give you a brief breakdown.

00:50 Go to stat, then go to edit, then go to list, you know, and just type your data and list one.

01:00 It doesn't have to be list one, but it could be, you know, any list.

01:08 Now after you do that, you're going to then again go to stat.

01:14 Then you're going to go to calc in your graphing calculator.

01:21 And then you're going to go to the one variable statistics function, one variable stats.

01:32 And then from there, you're going to type l1, press enter, and you're going to get all these statistics.

01:41 You'll get the mean, standard deviation, like five number summary, all that.

01:51 But what we really need is a mean and standard deviation.

01:54 So let's write that down.

01:55 So we compute it.

01:56 You'll get the mean is 20.

02:00 We get the standard deviation is about 6 .78.

02:08 Now if you're wondering which one to use, you'll see another one that has sigma sub -x.

02:14 Like this you'll probably see it 6 .49 the sigma sub x this one's for a population this is for um if your problem says explicitly you know we know the population center deviation you use that one but you know in real situations you don't so just use the you know the one with the lowercase as because that's for the sample center deviation unless your professor or teachers mentioned something about that but in most cases it's going to be you know the sample center deviation that you're going to use okay now we have to figure out what our t star value is so to find our t star value you're gonna need to figure out your degrees of freedom degrees of freedom is gonna be one less than your sample size is the degrees of freedom is n minus one so in this case it'll be 12 minus one which will be 11 and then you're gonna go table you're gonna go table b or you can use your own calculator if it has one sometimes that's maybe more confusing but go to table b and then just look for the 90 % comment interval on the bottom it's also just the value with you know 5 % of the area so left but again make sure you match up with the row that has a degree of freedom of 11 and then from there you'll you can see that you'll find that your that your t star value will be look 1 .76...

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