The relationship between hours studied and GPA:
The predictor variable is the variable named “study” denoting the number of hours studied by the student.
The criterion variable is the variable named “GPA” denoting the GPA of the student.
The hypothesis states that the GPA scores of the student is affected by the hours studied by the student. The null and alternate hypothesis can be therefore written as:
The critical value is given by the inverse of t-statistic with n-2 or 27 degrees of freedom and alpha value equal to 0.05. The critical value was determined to be 2.0518.
The statistic of interest to test the hypothesis is given by . The Pearson’s correlation coefficient, r, given by , was computed as 0.7539. The data has 29 sample points. Thus the statistic was computed to have the value 5.9628.
The test suggests rejection of null hypothesis at 5% level of significance since the statistic has value greater than the critical value.
The value of is 0.4316, which is the effect that the predictor variable has on the criterion variable. It denotes the proportion of variation in criterion variable as explained by the predictor variable.
The slope, given by , where is the standard deviation of the predictor X and is the sum of squared deviation from mean for the criterion variable was found to be 0.1024.
The intercept a given by was found to be 1.632 where is the mean of the criterion variable and is the mean of predictor.
The regression line was thus obtained as:
Putting X as 4 in the equation specified in part c, the predicted GPA was found to be 2.042.
Putting X as 8 in the equation specified in part c, the predicted GPA was found to be 2.4519.
Putting X as 12 in the equation specified in part c, the predicted GPA was found to be 2.862.
Putting X as 16 in the equation specified in part c, the predicted GPA was found to be 3.272
Putting X as 20 in the equation specified in part c, the predicted GPA was found to be 3.681.
The sum of squares for error in predictions was found to be 7.282
The regression sum of squares was found to be 9.59
The relationship between hours worked and GPA:
The predictor variable is the variable named “work” denoting the number of hours worked by the student.
The criterion variable is the variable named “GPA” denoting the GPA of the student
The hypothesis states that the GPA scores of the student are affected by the hours worked by the student. The null and alternate hypothesis can be therefore written as:
H0 : ρ=0 against H1: ρ ≠0
The critical value is given by the inverse of t-statistic with n-2 or 27 degrees of freedom and alpha value equal to 0.05. The critical value was determined to be 2.0518.
The statistic of interest to test the hypothesis is given by. The Pearson’s correlation coefficient, r, given as, was computed as -0.3426. The data has 29 sample points. Thus the statistic was computed to have the value 1.8949.
The critical value was found to be greater than the value of the statistic. Therefore the test fails to reject the null hypothesis at 5% level of significance.
The value of is 0.882621, which is the effect that the predictor variable has on the criterion variable. It denotes the proportion of variation in criterion variable as explained by the predictor variable.
The slope, given by , where is the standard deviation of the predictor X and is the standard deviation of the criterion variable was found to -0.026.
The intercept a given by was found to be 3.3269 where is the mean of the criterion variable and is the mean of predictor.
Putting X as 28 in the equation specified in part c, the predicted GPA was found to be 2.598
Putting X as 24 in the equation specified in part c, the predicted GPA was found to be 2.703.
Putting X as 16 in the equation specified in part c, the predicted GPA was found to be 2.9108.
Putting X as 12 in the equation specified in part c, the predicted GPA was found to be 3.0148.
Putting X as 8 in the equation specified in part c, the predicted GPA was found to be 3.1188.
The sum of squares error was computed as 14.892.
The regression sum of squares was found to be 1.9805.
The relationship between hours worked and hours studied:
The predictor variable is the variable named “work” denoting the number of hours worked by the student.
The criterion variable is the variable named “study” denoting number of hours studied by the student
The hypothesis states that the hours studied by the student are affected by the hours worked by the student. The null and alternate hypothesis can be therefore written as:
H0 : ρ=0 against H1: ρ ≠0
The critical value is given by the inverse of t-statistic with n-2 or 27 degrees of freedom and alpha value equal to 0.05. The critical value was determined to be 2.0518.
The statistic of interest to test the hypothesis is given by . The Pearson’s correlation coefficient, r, given by , was computed as –0.235. The data has 29 sample points. Thus the statistic was computed to have the value 1.2563.
The critical value was found to be greater than the value of the statistic. Therefore the test fails to reject the null hypothesis at 5% level of significance. The null is therefore accepted.
The value of is 0.94476, which is the effect that the predictor variable has on the criterion variable. It denotes the proportion of variation in criterion variable as explained by the predictor variable.
The relationship between hours worked and hours studied for students with high conscientiousness:
The predictor variable is the variable named “study” denoting the number of hours studied by the students whose conscientiousness was reportedly high.
The criterion variable is the variable named “work” denoting the number of hours studied by the students whose conscientiousness was reportedly high.
The Pearson’s correlation coefficient, r, given by was found to be 0.1739.
The value of is 0.94476, which is the effect that the predictor variable has on the criterion variable. It denotes the proportion of variation in criterion variable as explained by the predictor variable.
The relationship between hours worked and hours studied for students with low conscientiousness:
The predictor variable is the variable named “study” denoting the number of hours studied by the students whose conscientiousness was reportedly low.
The criterion variable is the variable named “work” denoting the number of hours studied by the students whose conscientiousness was reportedly low.
Calculate the statistic.
The Pearson’s correlation coefficient, r, given by was found to be -0.6220.
The value of is 0.61303, which is the effect that the predictor variable has on the criterion variable. It denotes the proportion of variation in criterion variable as explained by the predictor variable.
It can thus be seen that a student who invests more hours to studying has more GPA scores that those who invest lesser hours. However, not enough evidence was found that change in length of working hours would correspond with change in GPA scores. The data failed to provide any evidence to support the conjecture that longer working hours corresponded with shorter lengths time invested to studying. Again, it was seen that students with high conscientiousness showed positive association between study hours and work hours while those with low conscientiousness depicted negative association. Hence it is concluded that amount of time invested to studying does in fact affect GPA score, however, provided that the student is conscientious, work would not negatively impact his or her studies and hence GPA scores.
Essay Writing Service Features
Our Experience
No matter how complex your assignment is, we can find the right professional for your specific task. Contact Essay is an essay writing company that hires only the smartest minds to help you with your projects. Our expertise allows us to provide students with high-quality academic writing, editing & proofreading services.
Free Features
Free revision policy
$10Free bibliography & reference
$8Free title page
$8Free formatting
$8How Our Essay Writing Service Works
First, you will need to complete an order form. It's not difficult but, in case there is anything you find not to be clear, you may always call us so that we can guide you through it. On the order form, you will need to include some basic information concerning your order: subject, topic, number of pages, etc. We also encourage our clients to upload any relevant information or sources that will help.
Complete the order form
Once we have all the information and instructions that we need, we select the most suitable writer for your assignment. While everything seems to be clear, the writer, who has complete knowledge of the subject, may need clarification from you. It is at that point that you would receive a call or email from us.
Writer’s assignment
As soon as the writer has finished, it will be delivered both to the website and to your email address so that you will not miss it. If your deadline is close at hand, we will place a call to you to make sure that you receive the paper on time.
Completing the order and download