THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below.
-For the given data,which of the following is the result of the hypothesis test?
A)Since the test statistic equals 4.439 and the critical value equals 1.645,we reject the null hypothesis and assume there is a positive correlation between the variables.
B)Since the test statistic equals 4.113 and the critical value equals -1.645,we fail to reject the null hypothesis and assume there is no correlation between the variables.
C)Since the test statistic equals 3.305 and the critical value equals 2.447,we reject the null hypothesis and assume there is a correlation between the variables.
D)Since the test statistic equals 3.707 and the critical value equals 1.943,we reject the null hypothesis and assume there is a positive correlation between the variables.

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A professor of statistics is interested in studying the relationship between the number of hours graduate students spent studying for his comprehensive final exam and the exam score.The results of the regression analysis of hours studied on exam scores are presented below. 
-For the given data,which of the following is the result of the hypothesis test?
A)Since the test statistic equals 4.439 and the critical value equals 1.645,we reject the null hypothesis and assume there is a positive correlation between the variables. 
B)Since the test statistic equals 4.113 and the critical value equals -1.645,we fail to reject the null hypothesis and assume there is no correlation between the variables. 
C)Since the test statistic equals 3.305 and the critical value equals 2.447,we reject the null hypothesis and assume there is a correlation between the variables. 
D)Since the test statistic equals 3.707 and the critical value equals 1.943,we reject the null hypothesis and assume there is a positive correlation between the variables.

Quizplus · Accepted Answer

The null hypothesis in this case is that there is no correlation between the number of hours studied and exam scores i.e. β₁=0. The alternative hypothesis is that there is a positive correlation i.e. β₁>0. The test statistic is given as 3.707 and the critical value at 0.05 significance level and 22 degrees of freedom is 1.943. Since the test statistic value (3.707) is greater than the critical value (1.943), we reject the null hypothesis and assume there is a positive correlation between the number of hours studied and the exam scores. Therefore, the correct answer is D.