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The following table is a random sample looking at the average GPA of students, ard' the number of times they have been absent: Make scatter plot of the data an...

Question

The following table is a random sample looking at the average GPA of students, ard' the number of times they have been absent: Make scatter plot of the data and use linear regression to write a function that models the data: Also; state the correlaiicn coefficient for this linear regression and whether you believe your model is 8o3d fic for the data:AbsencesGPA 3.9 4.0 3,9 3.7 3.6 3.6 30 2.8 25 22

The following table is a random sample looking at the average GPA of students, ard' the number of times they have been absent: Make scatter plot of the data and use linear regression to write a function that models the data: Also; state the correlaiicn coefficient for this linear regression and whether you believe your model is 8o3d fic for the data: Absences GPA 3.9 4.0 3,9 3.7 3.6 3.6 30 2.8 25 22



Answers

The mean age of graduate students at a University is at most 31 y ears with a standard deviation of two years. A random sample of 15 graduate students is taken. The sample mean is 32 years and the sample standard deviation is three years. Are the data significant at the 1$\%$ level? The p-value is $0.0264 .$ State the null and alternative hypotheses and interpret the $p$ -value.

So in this question, were given a pie chart with a bunch of values and were asked to calculate the mean and the standard deviation for the sample. So to do that, let's go ahead and make our frequency distribution charge. So let's start with. Since this is a grouped data, we're going to take the midpoint off each class as our value off X. So we have X. The midpoint off 0 to 4 hours is too. 5 to 9 is seven 10 to 14 is 12 15 to 1917 22 24 22 25 to 29 is 27. And for 30 plus hours we're told to list the midpoint as 32. So we have our values off X. Now we're going to put our frequencies in. So we have five, 12, 24 17, 16, 11 and five. So we have all of our X and our frequency values. Now we're going to compute x times f. We have X f and for that we're going to get five times two is 10 12 times seventies 84 24 times 12 is 288 17 time 17 29 22 times. 16 3 52 21 20 Picture 27 27 times 11 He had 297 and then 32 times 51 16. So we get X times have over here, and our formula for the mean is basically the some off next times f over our number off values. So we're basically going to sum everything in this column and in this column, and we're going to computer mean? And so in this column was some this 1480 number of values. We have this 19, so we take one for 80 divided by 90 which gives us the sample. Mean off 16.44 So that's our first answer for the second one. We need to find standard deviation. So let's go ahead and expand this table out Basically what we have to calculate here. IHS X minus the main affects. Then we're going to square that remember going to multiply that by them frequency, and from there we can calculate the sample Standard division. The formula for the standard deviation is basically the some off X minus X squared times F divide by and minus one and the square root off this whole thing. So let's go ahead and calculate this value. This one we know is 89. So this value let's go ahead and calculate from this column over here. So just to remind ourselves the mean effects waas 16.44 eso to calculate this we take X which is two minus 16.44 Then we square it and we multiplied by five. Which gives us 1042.56 Yeah. Now here we have seven minus 16.44 squared times 12. 10 69 0.3632 Then we have 12, minus 16.44 squared times 24 Just 473 point 1264 and 17 minus 16.44 The whole thing squared times the frequency which is 17. 5.3312 Then we have here 22 minus 16.44 squared times 16 Just 494 points 176 Then we have 27 minus 16.44 squared times 11 12 to 6.6496 Then our last value 30 to minus 16.44 squared times five 1 to 10.568 And the sum of all of these values gives us well, you off. It gives us 55 to 2.24 So we're gonna put that into our standard deviation. So we have 55 to 2.24 He divided by n minus one. And then we take the square root and we get for our standard deviation 7.877 approximate to three decimal places, which gives us the mean and standard deviation from this sample.

Okay, so we know that the mean and standard deviation Incoming freshmen's high school GPS are you is 3.4 some deviation is your 35 on that? They're 25 students. The first step is to just check for the conditions read demonisation condition on 10% tradition. Okay, So the right for the radicalization condition, we can assume that the sample size is independent and randomly selected population on for a 10% condition. We can assume that 25 students is less than 10% of all students. So now we know that it is okay to use the a normal model to describe the sample distribution model because according to essential limit here, t the theoretical mean and standard deviation for the sample size. And are you on signal over and respectively, where you is the truth Mean and Sigma's truce, that education So the theoretical mean GPS for one of these seminar groups and a standard deviation for the sample size. And he is equal to 25 Can you tell us is equal to you four standard deviation. Why is equal to signal over which is your 0.35 five? Does your yourself. Okay, Now we just have to use to 68 95 1917 68 five percent route. It just says that distribution is union model symmetric union model. No trick. Then approximately 68% of observations will be within one standard deviation of the mean 95% 2 standard deviations. Nine Inference. Three standard deviations from the meat. So this means that approximately 68% of the observations will mean freshman high school GPS between 333 3.47 Because that's just two standard deviations from the mean on approximately 99.7% of the GPS observed nine and 3.61 that's just three. Standard deviations from the mean on 68% will be between do you point to six on 3.54


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