The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables number of years spent by the student at the university and score on the first midterm have a sample correlation coefficient r of about -0.36. Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. B H, : H, 0 D=0 OSO (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) O and (e) Based on the data, can the professor conclude (using the 0.05 level) that there is a significant linear relationship between number of years spent at the university and score on the first midterm? Yes No
The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables number of years spent by the student at the university and score on the first midterm have a sample correlation coefficient r of about -0.36. Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient p. (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. B H, : H, 0 D=0 OSO (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.) O and (e) Based on the data, can the professor conclude (using the 0.05 level) that there is a significant linear relationship between number of years spent at the university and score on the first midterm? Yes No
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables, number of years spent by the student at the university and score on the first midterm, have a sample correlation coefficient \( r \) of about \(-0.36\).
Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient \( \rho \). (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \]
\[ H_1: \]
(b) Determine the type of test statistic to use.
\[ \text{(Choose one)} \]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \]
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
\[ \]
\[ \]
(e) Based on the data, can the professor conclude (using the 0.05 level) that there is a significant linear relationship between number of years spent at the university and score on the first midterm?
\[ \text{Yes} \]
\[ \text{No} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F72744a26-05c1-48a5-a531-8ad8228a0d8f%2Fd4b78571-8999-4e6f-94bd-86620bcb7868%2Fi6o82q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The professor of an introductory statistics course has found something interesting: there is a small correlation between scores on his first midterm and the number of years the test-takers have spent at the university. For the 55 students taking the course, the professor found that the two variables, number of years spent by the student at the university and score on the first midterm, have a sample correlation coefficient \( r \) of about \(-0.36\).
Test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population correlation coefficient \( \rho \). (Assume that the two variables have a bivariate normal distribution.) Use the 0.05 level of significance, and perform a two-tailed test. Then complete the parts below.
(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).
\[ H_0: \]
\[ H_1: \]
(b) Determine the type of test statistic to use.
\[ \text{(Choose one)} \]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[ \]
(d) Find the two critical values at the 0.05 level of significance. (Round to three or more decimal places.)
\[ \]
\[ \]
(e) Based on the data, can the professor conclude (using the 0.05 level) that there is a significant linear relationship between number of years spent at the university and score on the first midterm?
\[ \text{Yes} \]
\[ \text{No} \]
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