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 $μ = 514$ . The teacher obtains a random sample of 2000 students, puts them through the review class, and finds that the mean math score of the 2000 students is 521 with a standard deviation of 111 . Complete parts (a) through (d) below.
(a) State the null and alternative hypotheses.
$H_{0} ◻ \nabla ◻ ◻, H_{1} : ◻ ◻ ◻$

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Final Answer: $H_{0} : μ = 514, H_{1} : μ > 514$

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Step 1 ：The null hypothesis (H0) is the statement that the teacher's claim is not true, i.e., the mean score after the review course is still 514. The alternative hypothesis (H1) is the statement that the teacher's claim is true, i.e., the mean score after the review course is greater than 514.

Step 2 ：Final Answer: $H_{0} : μ = 514, H_{1} : μ > 514$

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