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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

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.FOM: Focus On Modeling: Fitting Lines To Data
Problem 10P
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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 +0.0020x. 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 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 Ho and the alternative hypothesis H₁. Ho 0 H₁ :0 (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 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 ß XI 010 ロミロ O>O X Р ロ=ロ ☐#0 H OSO O<O
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 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 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 Ho and the alternative hypothesis H₁. Ho 0 H₁ :0 (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 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 ß XI 010 ロミロ O>O X Р ロ=ロ ☐#0 H OSO O<O
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