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# Hypothesis Testing

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I) State the null and alternate hypothesis.
II) Determine the rejection region. For example "if {see attachment}, then reject {see attachment}".
III) Determine the Test Statistic.
IV) Conclude either "Reject " or "Do not reject " based on your analysis and answer the question (either YES or NO) .
V) Determine the p value of the test.

At the Kinglet School District, the average score over the past 5 years for the math portion of the Scholastic Aptitude Test (SAT) was 511. An educator believes that recent changes to the curriculum have resulted in improved scoring on this test. In an attempt to verify this she gathers a SRS of 12 students and has them take the math portion of the SAT with the following results

520 480 550 610 490 500 510 550 560 480 500 530

Does this evidence support the educator's claim that the scores have improved at her school at the 5% significance level?________

##### Solution Summary

I) State the null and alternate hypothesis.
II) Determine the rejection region. For example "if {see attachment}, then reject {see attachment}".
III) Determine the Test Statistic.
IV) Conclude either "Reject " or "Do not reject " based on your analysis and answer the question (either YES or NO) .
V) Determine the p value of the test.

At the Kinglet School District, the average score over the past 5 years for the math portion of the Scholastic Aptitude Test (SAT) was 511. An educator believes that recent changes to the curriculum have resulted in improved scoring on this test. In an attempt to verify this she gathers a SRS of 12 students and has them take the math portion of the SAT with the following results

520 480 550 610 490 500 510 550 560 480 500 530

Does this evidence support the educator's claim that the scores have improved at her school at the 5% significance level?________

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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