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A local college requires an English composition course for all freshmen. This yeàr they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semes-

A local college requires an English composition course for all freshmen. This yeàr they are evaluating a new online version of the course. A random sample of n = 16 freshmen is selected and the students are placed in the online course. At the end of the semes-

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section11.4: Collecting Data
Problem 3E
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### Educational Synopsis for College Composition Course Evaluation #### Problem 5: Evaluation of New Online English Composition Course A local college requires all freshmen to take an English composition course. This year, a new online version of the course is being evaluated. The study involves a random sample of \( n = 16 \) freshmen who are placed in the online course. At the end of the semester, all freshmen take the same English composition exam. The sample's average score is \( M = 76 \). For the population of freshmen who attend the traditional lecture class, exam scores follow a normal distribution with a mean \( \mu = 80 \). **Research Questions:** - **(a)** If the traditional class exam scores have a standard deviation of \( \sigma = 12 \), does the sample provide sufficient evidence to conclude that the new online course significantly differs from the traditional course? - **Conditions:** Use a two-tailed test with \( \alpha = .05 \). - **(b)** If the population standard deviation is \( \sigma = 6 \), is the sample sufficient to demonstrate a significant difference? - **Conditions:** Again, assume a two-tailed test with \( \alpha = .05 \). - **(c)** Considering your answers for parts (a) and (b), explain how the standard deviation magnitude affects the hypothesis test outcome. ### Explanation of Hypotheses and Significance Tests 1. **Setting the Hypotheses:** - Null Hypothesis (\( H_0 \)): The mean score of the online course (\( M \)) is equal to the mean score of the traditional course (\( \mu \)). - Alternative Hypothesis (\( H_a \)): There is a significant difference between the online course mean score (\( M \)) and the traditional course mean score (\( \mu \)). 2. **Calculating the Test Statistic:** - The test statistic helps determine if the sample mean differs significantly from the population mean. - Use the formula for the test statistic \( Z = \frac{M - \mu}{\sigma / \sqrt{n}} \). 3. **Critical Value and Decision Rule:** - Identify the critical value for \( \alpha = .05 \) in a two-tailed test. - Compare the test statistic to the critical value to decide whether to reject \( H_0 \). 4. **Influence of Standard De
Transcribed Image Text:### Educational Synopsis for College Composition Course Evaluation #### Problem 5: Evaluation of New Online English Composition Course A local college requires all freshmen to take an English composition course. This year, a new online version of the course is being evaluated. The study involves a random sample of \( n = 16 \) freshmen who are placed in the online course. At the end of the semester, all freshmen take the same English composition exam. The sample's average score is \( M = 76 \). For the population of freshmen who attend the traditional lecture class, exam scores follow a normal distribution with a mean \( \mu = 80 \). **Research Questions:** - **(a)** If the traditional class exam scores have a standard deviation of \( \sigma = 12 \), does the sample provide sufficient evidence to conclude that the new online course significantly differs from the traditional course? - **Conditions:** Use a two-tailed test with \( \alpha = .05 \). - **(b)** If the population standard deviation is \( \sigma = 6 \), is the sample sufficient to demonstrate a significant difference? - **Conditions:** Again, assume a two-tailed test with \( \alpha = .05 \). - **(c)** Considering your answers for parts (a) and (b), explain how the standard deviation magnitude affects the hypothesis test outcome. ### Explanation of Hypotheses and Significance Tests 1. **Setting the Hypotheses:** - Null Hypothesis (\( H_0 \)): The mean score of the online course (\( M \)) is equal to the mean score of the traditional course (\( \mu \)). - Alternative Hypothesis (\( H_a \)): There is a significant difference between the online course mean score (\( M \)) and the traditional course mean score (\( \mu \)). 2. **Calculating the Test Statistic:** - The test statistic helps determine if the sample mean differs significantly from the population mean. - Use the formula for the test statistic \( Z = \frac{M - \mu}{\sigma / \sqrt{n}} \). 3. **Critical Value and Decision Rule:** - Identify the critical value for \( \alpha = .05 \) in a two-tailed test. - Compare the test statistic to the critical value to decide whether to reject \( H_0 \). 4. **Influence of Standard De
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