Question

# A new SAT study course is tested on 12 individuals. Pre-course and post-course scores are recorded....

A new SAT study course is tested on 12 individuals. Pre-course and post-course 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 NOTE: 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, you must first prove that assumption, though.)

 Pre-course score Post-course score 1230 1340 940 930 1090 1140 840 880 1100 1070 1250 1320 860 860 1330 1370 790 770 990 1040 1110 1200 740 850

PART A) State the null hypothesis.  H0: μd ≤ 0

PART B) State the alternative hypothesis. Ha: μd = 0

PART C) In words, state what your random variable Xd represents.-->The variable Xd represents the sample mean difference in SAT scores before the course and after the course.

PART D) State the distribution to use for the test. t={12-1}

PART E) What is the test statistic?

PART F) What is the p-value?  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 41.67.

PART G) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value

PART H) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.

α = 0.05. reject the null hypothesis. Since p-value < α, we reject the null hypothesis.

There is sufficient evidence to show that the average post-course SAT score is larger than the average pre-course SAT score.

PART I) Explain how you determined which distribution to use.

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