### Comparing Midterm Scores: Fall vs. Spring SemesterMr. Bates wants to compare the midterm scores of his students who took the course during the fall semester versus the spring semester. Below is the data he collected:#### Fall Semester Scores:89, 86, 64, 91, 92, 94, 87, 83, 86, 90, 74, 59, 87, 97, 87#### Spring Semester Scores:76, 70, 82, 94, 76, 66, 72, 51, 75, 97, 74, 81, 85, 96, 74**Research Question:**Can Mr. Bates conclude that his fall students scored better on average than his spring students? Use a significance level of α = 0.10.**Hypothesis Testing Steps:**1. **Type of Test:** - Determine whether a one-sample or two-sample test is appropriate and whether it should be a t-test or z-test based on sample sizes and availability of population standard deviations.2. **Null Hypothesis (\(H_0\)):** - The null hypothesis typically states that there is no difference between the two groups. In this case, it would state that the mean midterm scores for the fall and spring semesters are equal. \[ H_0: \mu_{Fall} = \mu_{Spring} \]3. **Alternate Hypothesis (\(H_a\)):** - The alternate hypothesis reflects the research question, suggesting that the fall students scored better than the spring students. \[ H_a: \mu_{Fall} > \mu_{Spring} \]4. **Standard Error (SE):** - Calculate the standard error of the difference between the two sample means.5. **Test Statistic:** - Compute the test statistic (e.g., t-score).6. **P-value:** - Determine the p-value corresponding to the test statistic.7. **Decision:** - Compare the p-value to the significance level (\( \alpha \)) to make a decision. If the p-value is less than or equal to \( \alpha \), you reject the null hypothesis. Otherwise, you fail to reject it.8. **Conclusion Sentence:** - Write a conclusion sentence summarizing whether the fall students scored

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Description: ### Comparing Midterm Scores: Fall vs. Spring SemesterMr. Bates wants to compare the midterm scores of his students who took the course during the fall semester versus the spring semester. Below is the data he collected:#### Fall Semester Scores:89,

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Statistics

2. Mr. Bates wants to compare the midterm scores of his students who took during the fall semester versus the spring semester. Here is the data: Fall 89 86 64 91 92 94 87 83 86 90 74 59 87 97 87 Spring 76 70 82 94 76 66 72 51 75 97 74 81 85 96 74 Can he say that his fall students scored better than his spring students? (Use a = .10) Type of Test: Null Hypothesis: Alternate Hypothesis:

2. Mr. Bates wants to compare the midterm scores of his students who took during the fall semester versus the spring semester. Here is the data: Fall 89 86 64 91 92 94 87 83 86 90 74 59 87 97 87 Spring 76 70 82 94 76 66 72 51 75 97 74 81 85 96 74 Can he say that his fall students scored better than his spring students? (Use a = .10) Type of Test: Null Hypothesis: Alternate Hypothesis:

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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