A new SAT study course is tested on 12 individuals. Precourse and postcourse scores are recorded. Of interest is the average increase in SAT scores. The following data is collected. Conduct a hypothesis test at the 5% level. Pre-course score Postcourse score 1250 1320 990 920 1040 1110 840 880 1100 1070 1250 1320 860 860 1330 1370 790 770 990 1040 1110 1200 740 850 NOTE: If you are using a Student's tdistribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must rst prove that assumption, though.) What is the test statistic? (If using the 2 distribution round your answer to two decimal places, and if using the tdistribution round your answer to three decimal places.) t V= El Part (f) What is the pvalue? (Round your answer to four decimal places.) : Explain what the pvalue means for this problem. 0 If H0 is false, then there is a chance equal to the pvalue that the sample average difference between the post-course scores and precourse scores is less than 35.00. 0 If H0 is true, then there is a chance equal to the p-value that the sample average difference between the post-course scores and pre-course scores is less than 35.00. 0 If H0 is false, then there is a chance equal to the pvalue that the sample average difference between the post-course scores and precourse scores is at least 35.00. C) If H0 is true, then there is a chance equal to the p-Value that the sample average difference between the post-course scores and pre-course scores is at least 35.00. J Correct! A p-value is the probability that an outcome of the data will happen purely by chance when Hg is true