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Urilverslly Interesied In Iracking Its honcrs program belleves Ihal the proportlon of graduates wllh a GPA of 3.00 or below less than 0.20. In" sample of 200 g...

Question

Urilverslly Interesied In Iracking Its honcrs program belleves Ihal the proportlon of graduates wllh a GPA of 3.00 or below less than 0.20. In" sample of 200 graduates, 30 students have a GPA of 3.00 or below The value of Ihe test statislic and Its associated p value at the 5%6 signllicance level are respecllvely:Muitple Cholce[199 4177 and pvulue 00385'199 F77 arid pvalua 00770771 and P vdlue 0,0985177 ano pvole 0ot70

urilverslly Interesied In Iracking Its honcrs program belleves Ihal the proportlon of graduates wllh a GPA of 3.00 or below less than 0.20. In" sample of 200 graduates, 30 students have a GPA of 3.00 or below The value of Ihe test statislic and Its associated p value at the 5%6 signllicance level are respecllvely: Muitple Cholce [199 4177 and pvulue 00385 '199 F77 arid pvalua 00770 771 and P vdlue 0,0985 177 ano pvole 0ot70



Answers

IQ and grades Exercise 3 (page 158$)$ included the plot shown below of school grade point average
$(\mathrm{GPA})$ against 1$Q$ test score for 78 seventh-grade students. (GPA was recorded on a 12 -point scale with $\mathrm{A}+=12, \mathrm{A}=11, \mathrm{A}-=10, \mathrm{B}+=9, \ldots, \mathrm{D}-=1$ and $\mathrm{F}=0 .$ . Calculation shows that the mean and standard deviation of the 1 $\mathrm{Q}$ scores are $\overline{x}=108.9$ and $s_{x}=13.17 .$ For the GPAs, these values are $\overline{y}=$ 7.447 and $s_{y}=2.10 .$ The correlation between 1 $\mathrm{Q}$ and
GPA is $r=0.6337 .$
(a) Find the equation of the least-squares line for predicting GPA from 1$Q$ . Show your work.
(b) What percent of the observed variation in these students' GPAs can be explained by the linear relationship between GPA and IQ?
(c) One student has an IQ of 103 but a very low GPA of 0.53 . Find and interpret the residual for this
student.

In this problem, using the person's X. Probabilities, we have to find the probability that the students applied to more than three colleges, Probability that the students applied to more than three colleges. Yes, probability off X. Mhm Greater than three. This is equal to probably be off 4-6 colleges, blessed probability off mm seven or more colleges. Because more than three colleges means either 4-6 colleges Or seven or more colleges. This is equal to Probability debt the student applied 4-6 colleges is 0.37. So 0.37 plus Probability that the student applied to seven or more colleges is 0.35. So 0.35, 0.37 plus 0.35 is equal to 0.72. So the probability that the student applied to more than three colleges is 0.72.

In this problem, using the persons as probabilities, we have to find the probability that the student applied to at least two colleges, Probability debt the student applied to at least two colleges is the probability of X Greater than or equal to two. This is equal to probability off two or three colleges bless probably T. O. 4-6 colleges Plus the probability of seven or more colleges. Because at least two colleges means that Either toward three colleges or 4-6 colleges or seven or more colleges. Now this is equal to Probability of two or 3 colleges is 0.18. So this is 0.18 plus Probability of 4- six colleges is 0.37. So 0.37 plus prosperity of seven or more colleges is 0.35 So 0.35. Mhm. Okay. That is 0.18 plus 0.37 plus 0.35. This is equal to zero point 90 Mhm. So the probability debt the students applied to at least two colleges is 0.90

In this question here for part A. We want to find to the nearest 10th B average G p A. Of a student who does know studying. So that's when h is you go to zero. So g of zero is equal to zero point 006 times zero squared plus 0.2 come zero plus 1.2, which is equal to 1.2 carpi. Here we want to find gpm, assume who studies 12 hours. So that's G 0 12 So instead of plugging and zero for each, we plug in 12. So 0.6 times 12 squared pluses. Europeans here, too. Times 12 plus 1.2, which is equal to approximately 2.3. Now, what part C Here we want to find how many hours of studying a required to achieve 3.2. So that means that 3.2 his equal to 0.6 each squared classes your 0.2 h plus 1.2 subtracting 3.2 from both sides of the equation. You got 0.6 h squared plus 0.2 h minus two is you go to the room. Then he used the quadratic formula to solve for when h is equal to zero or what makes a secretion true. So we have a is equal to 0.6 b is equal to 0.2 and C is equal to negative two. And what you'll get is that like your two solutions are 16 points at 667 or negative 20 but obviously are which cannot be negative. 20 because you cannot study negative number of hours, so your solution would be 16.667

In this problem, using the persons as probabilities, we have to find the probability that the student applied to know colleges probability debt the student applied to know colleges is probability of X equal to zero. In the given table. We can see that for no colleges, no probability is a sound, and so the probability that the student applied to know colleges is equal to zero, which is our required answer.


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