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# 1) A NEW SAT STUDY COURSE IS TESTED ON 12 INDIVIDUALS. PRE-COURSE

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Author: Christine Farr
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1) A new SAT study course is tested on 12 individuals. Pre-course and post-coursescores are recorded. Of interest is the average increase in SAT scores. The followingdata is collected. Conduct a hypothesis test at the 5% level.Pre-course scorePost-course score1200132094092010301130840880110010701250132086086013301370790770990104011101200740850NOTE: If you are using a Student's t-distribution for the problem, including for paired data,you may assume that the underlying population is normally distributed. (In general, youmust first prove that assumption, though.)Part (a)State the null hypothesis.H0: μd < 0H0: μd ≤ 0H0: μd > 0H0: μd ≠ 0Part (b)State the alternative hypothesis.Ha: μd = 0Ha: μd > 0Ha: μd ≠ 0Ha: μd < 0Part (c)In words, state what your random variablex´drepresents.The variablex´drepresents the sample mean difference in SAT scores before thecourse and after the course.The variablex´drepresents the population mean difference in SAT scores before thecourse and after the course.The variablex´drepresents the sample total difference in the scores before and afterthe course.The variablex´drepresents the population total difference in the scores before andafter the course.Part (d)State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees offreedom.): ____Part (e)What is the test statistic? (Round your answer to two decimal places.)=Part (f)What is the p-value? (Round your answer to four decimal places.)

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