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A certain test preparation course is designed to improve students' SAT Math scores. The students who...

A certain test preparation course is designed to improve students' SAT Math scores. The students who took the prep course have a mean SAT Math score of 507 while the students who did not take the prep course have a mean SAT Math score of 501. Assume that the population standard deviation of the SAT Math scores for students who took the prep course is 45.7 and for students who did not take the prep course is 32.1 The SAT Math scores are taken for a sample of 78 students who took the prep course and a sample of 64 students who did not take the prep course. Conduct a hypothesis test of the claim that the SAT Math scores for students who took the prep course is higher than the SAT Math scores for students who did not take the prep course. Let μ1 be the true mean SAT Math score for students who took the prep course and μ2 be the true mean SAT Math score for students who did not take the prep course. Use a 0.05 level of significance.

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5 : Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5 : Find the p-value associated with the test statistic. Round your answer to four decimal places.


Step 4 of 5: Make the decision for the hypothesis test.

Step 5 of 5: State the conclusion of the hypothesis test.

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