A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with u=518. The teacher obtaips a random sample of 2200 students, puts them through the review class, and finds that the mean math score of the 2200 students is 525 with a standard deviation of 113. Complete parts (a) through (d) below. (a) State the null and alternative hypotheses. Ho: H - 518, H:P > 518 (b) Test the hypothesis at the a =0.10 level of significance. Is a mean math score of 525 statistically significantly higher than 518? Conduct a hypothesis test using the P-value approach. Find the test statistic. to =D (Round to two decimal places as needed.)

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**Title: Hypothesis Testing in Educational Research**

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**Scenario:**  
A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with a mean (μ) of 518. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of these 2200 students is 525 with a standard deviation of 113. Complete parts (a) through (d) below.

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**(a) State the null and alternative hypotheses.**

\[ H_0: \mu = 518 \]  
\[ H_1: \mu > 518 \]

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**(b) Test the hypothesis at the \(\alpha = 0.10\) level of significance. Is a mean math score of 525 statistically significantly higher than 518? Conduct a hypothesis test using the P-value approach.**

- **Find the test statistic:**

\[ t_0 = \boxed{} \]  
(Round to two decimal places as needed.)

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**Explanation of Graphs and Diagrams:**  
There are no graphs or diagrams associated with this text. Should any visuals be included, they would typically illustrate the distribution of test scores, the sampling distribution under the null hypothesis, or the critical value region for significance testing.

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**Note:** To complete the test, compute the test statistic \( t_0 \) using the formula for the one-sample t-test for means, and compare it to the critical value from the t-distribution table at the 0.10 significance level. Alternatively, use statistical software to identify the P-value and draw your conclusion based on whether the P-value is less than \(\alpha = 0.10\).
Transcribed Image Text:**Title: Hypothesis Testing in Educational Research** --- **Scenario:** A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with a mean (μ) of 518. The teacher obtains a random sample of 2200 students, puts them through the review class, and finds that the mean math score of these 2200 students is 525 with a standard deviation of 113. Complete parts (a) through (d) below. --- **(a) State the null and alternative hypotheses.** \[ H_0: \mu = 518 \] \[ H_1: \mu > 518 \] --- **(b) Test the hypothesis at the \(\alpha = 0.10\) level of significance. Is a mean math score of 525 statistically significantly higher than 518? Conduct a hypothesis test using the P-value approach.** - **Find the test statistic:** \[ t_0 = \boxed{} \] (Round to two decimal places as needed.) --- **Explanation of Graphs and Diagrams:** There are no graphs or diagrams associated with this text. Should any visuals be included, they would typically illustrate the distribution of test scores, the sampling distribution under the null hypothesis, or the critical value region for significance testing. --- **Note:** To complete the test, compute the test statistic \( t_0 \) using the formula for the one-sample t-test for means, and compare it to the critical value from the t-distribution table at the 0.10 significance level. Alternatively, use statistical software to identify the P-value and draw your conclusion based on whether the P-value is less than \(\alpha = 0.10\).
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