A random sample of 7 beef hotdogs was taken and the amount...

A random sample of 7 beef hotdogs was taken and the amount of sodium (in mg) and caloric content (in calories) were measured. The data are in the table below. Once you have entered the data into L1 and L2, go to 2-Var Stats on your T184 and enter L1 and L2 and scroll down. If you have entered the data correctly, you should see \(\sum xy = 627873\). caloric content sodium content 187 499 177 429 182 481 190 645 175 479 176 425 185 486 a) State the random variables. rv X = the Select an answer of a randomly selected Select an answer rv Y = the Select an answer of a randomly selected Select an answer

Transcript

00:01 All right.

00:01 So i can see that there are a few parts of the problem that are already done.

00:06 For instance, you have the regression line is y equals 80 .819 plus 2 .4715x.

00:19 For, let's see here.

00:21 So seeing where you have the blanks starting, we have that the correlation coefficient is 0 .9064.

00:30 The interpretation here is that because r is relatively close to 1, this is a strong, positive, linear correlation, lin -corps, for short.

00:49 Then we have r -squared to equal to 0 .82.

00:54 What that means in interpretation would be that 0 .82 times 100, or 82 .2%, or 82 .2 % of variation in y can be explained by variation in x then for the prediction we're asked to calculate the predicted value of sodium content when the hot dog has 130 calories so that's going to be 80 .819 actually i'll just type the numbers out on screen and calculate on screen so it's 80 .819 plus 2 .4715 times 130.

01:49 So we would predict 402 .114 milligrams of sodium.

02:01 And then lastly, for the t test of significance, the idea is that our null hypothesis is going to be that the slope of the regression line is equal to zero in the alternate hypothesis, that the slope of the regression line does not equal zero.

02:19 We have that t is going to be distributed, or yeah, our t value is going to be equal to our measured slope, or, yeah, our measured slope m minus m not.

02:34 Oh, actually, one second here, i'm just realizing with the information that we have available, i'm going to need to do a slightly different t test, actually.

02:41 Okay, so having just the r value, the null hypothesis is r equals zero, and the alternate is r does not equal zero.

02:52 Our t value is going to be equal to r times the square root of n minus 2 over 1 minus r squared...

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