(a) State the null and alternative hypotheses. Ho: H:

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**Math Review Course Effectiveness Analysis**

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 administrators of the exam, scores are normally distributed with a mean (μ) of 518. The teacher obtains a random sample of 2200 students, enrolls them in the review course, 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.**

- \(H_0\): The null hypothesis represents the situation where the review course has no effect on the scores. It can be denoted as \(H_0: \mu = 518\).
- \(H_1\): The alternative hypothesis represents the situation where the review course increases the scores. It can be denoted as \(H_1: \mu > 518\).

(Note: The placeholders next to \(H_0\) and \(H_1\) in the image are dropdown menus for selecting the appropriate symbols and values for forming the hypotheses.)

In this context, the hypothesis testing will help determine whether the observed increase in mean scores (from 518 to 525) can be attributed to the review course rather than random chance. Further steps in the analysis would typically include calculating the test statistic, determining the p-value, and comparing it against the significance level to make a conclusion about the hypotheses.
Transcribed Image Text:**Math Review Course Effectiveness Analysis** 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 administrators of the exam, scores are normally distributed with a mean (μ) of 518. The teacher obtains a random sample of 2200 students, enrolls them in the review course, 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.** - \(H_0\): The null hypothesis represents the situation where the review course has no effect on the scores. It can be denoted as \(H_0: \mu = 518\). - \(H_1\): The alternative hypothesis represents the situation where the review course increases the scores. It can be denoted as \(H_1: \mu > 518\). (Note: The placeholders next to \(H_0\) and \(H_1\) in the image are dropdown menus for selecting the appropriate symbols and values for forming the hypotheses.) In this context, the hypothesis testing will help determine whether the observed increase in mean scores (from 518 to 525) can be attributed to the review course rather than random chance. Further steps in the analysis would typically include calculating the test statistic, determining the p-value, and comparing it against the significance level to make a conclusion about the hypotheses.
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