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I need help solving this question, I am unsure how to compute a hypothesis test

I need help solving this question, I am unsure how to compute a hypothesis test

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
Problem 1P
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I need help solving this question, I am unsure how to compute a hypothesis test
--- ### Hypothesis Testing for Speed Reading Programs **Objective:** To evaluate the effectiveness of two speed reading programs by comparing the reading speeds of participants. **Procedure:** Ten pairs of people are randomly selected. For each pair, one person is randomly assigned to take Program 1, while the other person takes Program 2. After completing their respective programs, the reading speeds (in words per minute) for each participant are recorded for analysis. **Data Collected:** | Pair | Program 1 Speed (words per minute) | Program 2 Speed (words per minute) | |------|------------------------------------|------------------------------------| | 1 | 894 | 1032 | | 2 | 1055 | 1194 | | 3 | 1056 | 1096 | | 4 | 1125 | 1074 | | 5 | 996 | 1032 | | 6 | 1026 | 1091 | | 7 | 910 | 959 | | 8 | 971 | 1010 | | 9 | 1059 | 1091 | | 10 | 1092 | 1096 | **Hypothesis Test:** Using a 10% significance level (α = 0.10), we aim to determine if there is a statistically significant difference in the reading speeds between the two programs. **Assumptions:** Assume that the populations being sampled are approximately normally distributed. 1. **Null Hypothesis (H0):** The mean reading speeds for both programs are equal (no difference in effectiveness). 2. **Alternative Hypothesis (H1):** There is a difference in the mean reading speeds (one program is more effective than the other). **Next Steps:** - Calculate the differences between paired observations. - Perform a t-test for paired samples to compare the reading speeds. - Interpret the p-value to make a conclusion regarding the null hypothesis. **Conclusion:** The result of the hypothesis test will indicate whether there is sufficient evidence to conclude that there is a difference in the effectiveness of the two speed reading programs. --- This structured approach ensures a comprehensive analysis of the data leading to informed conclusions about the effectiveness of the speed reading programs.
Transcribed Image Text:--- ### Hypothesis Testing for Speed Reading Programs **Objective:** To evaluate the effectiveness of two speed reading programs by comparing the reading speeds of participants. **Procedure:** Ten pairs of people are randomly selected. For each pair, one person is randomly assigned to take Program 1, while the other person takes Program 2. After completing their respective programs, the reading speeds (in words per minute) for each participant are recorded for analysis. **Data Collected:** | Pair | Program 1 Speed (words per minute) | Program 2 Speed (words per minute) | |------|------------------------------------|------------------------------------| | 1 | 894 | 1032 | | 2 | 1055 | 1194 | | 3 | 1056 | 1096 | | 4 | 1125 | 1074 | | 5 | 996 | 1032 | | 6 | 1026 | 1091 | | 7 | 910 | 959 | | 8 | 971 | 1010 | | 9 | 1059 | 1091 | | 10 | 1092 | 1096 | **Hypothesis Test:** Using a 10% significance level (α = 0.10), we aim to determine if there is a statistically significant difference in the reading speeds between the two programs. **Assumptions:** Assume that the populations being sampled are approximately normally distributed. 1. **Null Hypothesis (H0):** The mean reading speeds for both programs are equal (no difference in effectiveness). 2. **Alternative Hypothesis (H1):** There is a difference in the mean reading speeds (one program is more effective than the other). **Next Steps:** - Calculate the differences between paired observations. - Perform a t-test for paired samples to compare the reading speeds. - Interpret the p-value to make a conclusion regarding the null hypothesis. **Conclusion:** The result of the hypothesis test will indicate whether there is sufficient evidence to conclude that there is a difference in the effectiveness of the two speed reading programs. --- This structured approach ensures a comprehensive analysis of the data leading to informed conclusions about the effectiveness of the speed reading programs.
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