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Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 62 freshmen and divides them into 31 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course. Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, Ho: μ = 0, against the alternative hypothesis, H₁: μ ‡ 0, where u is the mean course grade difference for the student population. The sample statistics for Diana's test are summarized in the table. Variable description traditional course grade new course grade difference (new- traditional) t = Sample mean Xtrad = 3.45773 = 3.32772 Xnew x = -0.13001 Sample standard deviation Strad = = 2.30766 Snew = 2.21794 s = 0.34221 Standard error estimate SEtrad 0.41447 SEnew = 0.39835 SE = 0.06146 = Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers. Compute the t-statistic for Diana's matched-pairs t-test. Provide your answer with precision to three decimal places.

Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 62 freshmen and divides them into 31 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course. Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, Ho: μ = 0, against the alternative hypothesis, H₁: μ ‡ 0, where u is the mean course grade difference for the student population. The sample statistics for Diana's test are summarized in the table. Variable description traditional course grade new course grade difference (new- traditional) t = Sample mean Xtrad = 3.45773 = 3.32772 Xnew x = -0.13001 Sample standard deviation Strad = = 2.30766 Snew = 2.21794 s = 0.34221 Standard error estimate SEtrad 0.41447 SEnew = 0.39835 SE = 0.06146 = Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers. Compute the t-statistic for Diana's matched-pairs t-test. Provide your answer with precision to three decimal places.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 62 freshmen and divides them into 31 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course. Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, Ho: μ = 0, against the alternative hypothesis, H₁: μ ‡ 0, where u is the mean course grade difference for the student population. The sample statistics for Diana's test are summarized in the table. Sample mean Variable description traditional course grade new course grade difference (new - traditional) t = Xtrad = 3.45773 Xnew = 3.32772 x = -0.13001 Sample standard deviation Strad = = 2.30766 Snew = 2.21794 s = 0.34221 Standard error estimate SEtrad 0.41447 SEnew = 0.39835 SE = 0.06146 = Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers. Compute the t-statistic for Diana's matched-pairs t-test. Provide your answer with precision to three decimal places.
Transcribed Image Text:Suppose Diana, an educational researcher at a local university, wants to test the impact of a new Spanish course that integrates cultural-immersion teaching techniques with standard teaching practices. She selects a simple random sample of 62 freshmen and divides them into 31 pairs, matched on IQ and high school GPA. She randomly selects one member of each pair to take the new course, while the other member in the pair takes the traditional course. Next, Diana records the course grade, tallied on a scale from 0 to 4, for all sample members at the end of the semester, and she computes the difference in grades between the members in each matched pair by subtracting the traditional course grade from the new course grade. She wants to determine if the new Spanish course improves or weakens student performance. She runs a matched-pairs t-test to test the null hypothesis, Ho: μ = 0, against the alternative hypothesis, H₁: μ ‡ 0, where u is the mean course grade difference for the student population. The sample statistics for Diana's test are summarized in the table. Sample mean Variable description traditional course grade new course grade difference (new - traditional) t = Xtrad = 3.45773 Xnew = 3.32772 x = -0.13001 Sample standard deviation Strad = = 2.30766 Snew = 2.21794 s = 0.34221 Standard error estimate SEtrad 0.41447 SEnew = 0.39835 SE = 0.06146 = Although Diana does not know the standard deviation of the underlying population of course grade differences, she assumes that the population is normally distributed because the sample data are symmetric, single-peaked, and contain no outliers. Compute the t-statistic for Diana's matched-pairs t-test. Provide your answer with precision to three decimal places.
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