(1)The results of the 2013 National Assessment of Educational Progress are in NAEP2013.csv grouped by jurisdiction (50 states + DC). Consider the participants to be a random sample of all students in the United States. The variable

G8mathchange2011 contains the change in Grade 8 average math scores for each jurisdiction from 2011 to 2013. A positive value means the average score for the jurisdiction increased from 2011 to 2013. You want to use this data to test whether the average Grade 8 math score nationwide changed from 2011 to 2013. Let denote the average Grade 8 math score nationwide.

(a)Always begin data analysis with an appropriate plot of the data. Start with a boxplot of the changes in Grade 8 average math scores for each jurisdiction from 2011 to 2013. Include the plot here and comment on it.

(b)It's also a good idea to produce summary statistics of your data. Calculate the sample mean and sample variance the set of math score changes. Include the output here.

(c)Now for the hypothesis test - what are the null and alternative hypotheses?

(d)Which test will you use, the t-test or z-test? What are the assumptions behind the test? Are they satisfied?

(e)Run the test and paste the output here.

(f)What conclusion do you reach? State the reasoning behind your conclusion and interpret your conclusion.

(g)Calculate a 95% confidence interval for = the average grade 8 math score nationwide. Paste the output here. Interpret the confidence interval - how does it elaborate upon the conclusion from the hypothesis test above?