1 according to the national automobile dealers association...

1- According to the National Automobile Dealers Association, the mean price for used cars is $10,192. A manager of Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership less than the national mean. The prices for the sample of 50 cars is in the sheet Question 3 in your data file. a) formulate the hypotheses that can be used to determine whether the population mean price for used cars at this particular dealership less than the national mean. b) What is the p value? c) At α= .05 what is your conclusion? on excel

Transcript

00:01 Our mu is equal to 10 ,192, and our alternative hypothesis would be the opposite of that.

00:06 So it would say our population mean is not equal to 10 ,192.

00:12 And also given in this problem is that our sample size, our n equals 50.

00:18 Now, here's an interesting situation.

00:20 In this problem, we're not given an x bar or an s in this problem.

00:28 We're not given a standard deviation either.

00:29 So how do we compute these? so for calculating x bar, we follow this formula.

00:40 X bar equals the sum of all the individual data points divided by the sample size.

00:49 So we're using the web file that the book provides us, we can calculate this sum, which is 487 ,500 divided by 50.

01:03 Now, if you want to use excel for this, you can use the following formula equals in all cap sum and then the range of the values.

01:14 So for me it was a1, a1 to a51.

01:20 And that evaluates to 9 ,750.

01:26 Now, to calculate the standard deviation, we use the following formula.

01:32 S is equal to the square root of the sum of the difference between each individual data point and the sample mean squared over n minus 1, and that is equal to 1 ,399 .99 .9.

01:55 If you wanted to do that in excel, you would do that in excel.

01:59 Do std -ev .s and then your data range, a1 to a -51.

02:15 So now that we have our s and our x -bar, we can compute a t -test statistic to find our p -value.

02:27 So to compute a t -test statistic, that is equal to our sample mean minus our population mean divided by our sample, standard deviation divided by the square root of our sample size, which is equal to 4 ,000 750 minus 10 ,192 over our sample standard deviation of 1 ,399 .99, divided by the square root of 50.

03:10 50 and this evaluates to roughly negative 2 .3 or negative 2 .23.

03:21 Okay, so if we draw our t distribution with t equals zero in the middle, this value would lie to the left of t equals zero somewhere here.

03:33 And we are interested in finding the area to the left of this t equals negative 2 .23.

03:41 This area represents probability that t is less than or equal to negative 2 .23.

03:48 Now, in order to find this probability value, we will need to compute a degrees of freedom.

03:55 So we take our n, so our degree of freedom is equal to n minus 1, which is equal to 49...

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