Suppose that we are examining the relationship between scores on a nationwide, standardized test and performance in college. We have chosen a random sample of 96 students just finishing their first year of college, and for each student we've recorded her score on the standardized test and her grade point average for her first year in college. For our data, the least-squares regression equation relating the two variables score on this standardized test (denoted by x and ranging from 400 to 1600) and first-year college grade point average (denoted by y and ranging from 0 to 4) is y=0.8884 +0.0020.x. The standard error of the slope of this least-squares regression line is approximately 0.0016. Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 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 H₁. Ho H, O (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.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average? O Yes O No В X 020 O
Suppose that we are examining the relationship between scores on a nationwide, standardized test and performance in college. We have chosen a random sample of 96 students just finishing their first year of college, and for each student we've recorded her score on the standardized test and her grade point average for her first year in college. For our data, the least-squares regression equation relating the two variables score on this standardized test (denoted by x and ranging from 400 to 1600) and first-year college grade point average (denoted by y and ranging from 0 to 4) is y=0.8884 +0.0020.x. The standard error of the slope of this least-squares regression line is approximately 0.0016. Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 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 H₁. Ho H, O (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.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average? O Yes O No В X 020 O
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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Question
![Suppose that we are examining the relationship between scores on a nationwide, standardized test and performance in college. We have chosen a random sample of 96 students just finishing their first year of college, and for each student we've recorded her score on the standardized test and her grade point average for her first year in college. For our data, the least-squares regression equation relating the two variables **score on this standardized test** (denoted by \( x \) and ranging from 400 to 1600) and **first-year college grade point average** (denoted by \( y \) and ranging from 0 to 4) is \(\hat{y} = 0.8884 + 0.0020x\). The standard error of the slope of this least-squares regression line is approximately 0.0016.
Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope \(\beta_1\).
(Assume that the variable \( y \) follows a normal distribution for each value of \( x \) and that the other regression assumptions are satisfied.) Use the 0.10 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 \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \blacksquare
\]
\[
H_1: \blacksquare
\]
(b) Determine the type of test statistic to use.
\[
\text{(Choose one)} \bigtriangledown
\]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[
\blacksquare
\]
(d) Find the \( p \)-value. (Round to three or more decimal places.)
\[
\blacksquare
\]
(e) Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average?
\[
\bigcirc \text{Yes} \quad \bigcirc \text{No}
\]
---
### Explanation of Graph or Diagram:
A sidebar is present showing various statistical symbols and notations that might be used to input or write mathematical equations and statistical symbols. It includes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c10e8ad-3433-42a7-ad9a-20db80d2b0e4%2F3ebe5dbd-2cd3-490f-9056-2723d3e43a32%2Fbafwub5_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that we are examining the relationship between scores on a nationwide, standardized test and performance in college. We have chosen a random sample of 96 students just finishing their first year of college, and for each student we've recorded her score on the standardized test and her grade point average for her first year in college. For our data, the least-squares regression equation relating the two variables **score on this standardized test** (denoted by \( x \) and ranging from 400 to 1600) and **first-year college grade point average** (denoted by \( y \) and ranging from 0 to 4) is \(\hat{y} = 0.8884 + 0.0020x\). The standard error of the slope of this least-squares regression line is approximately 0.0016.
Based on these sample results, test for a significant linear relationship between the two variables by doing a hypothesis test regarding the population slope \(\beta_1\).
(Assume that the variable \( y \) follows a normal distribution for each value of \( x \) and that the other regression assumptions are satisfied.) Use the 0.10 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 \( H_0 \) and the alternative hypothesis \( H_1 \).
\[
H_0: \blacksquare
\]
\[
H_1: \blacksquare
\]
(b) Determine the type of test statistic to use.
\[
\text{(Choose one)} \bigtriangledown
\]
(c) Find the value of the test statistic. (Round to three or more decimal places.)
\[
\blacksquare
\]
(d) Find the \( p \)-value. (Round to three or more decimal places.)
\[
\blacksquare
\]
(e) Based on the sample results, can we conclude (using the 0.10 level) that there is a significant linear relationship between score on the standardized test and first-year college grade point average?
\[
\bigcirc \text{Yes} \quad \bigcirc \text{No}
\]
---
### Explanation of Graph or Diagram:
A sidebar is present showing various statistical symbols and notations that might be used to input or write mathematical equations and statistical symbols. It includes
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