Investigation 4: 2021 Virginia and Maryland Math SAT Scores In 2021, a separate sample of 400 high school seniors was randomly taken from both Virginia (VA) and Maryland (MD) and each of their math SAT scores was recorded. We want to test whether there is a difference in math SAT scores for high school seniors between Virginia and Maryland at the 0.01 significance level. This data comes from the National Center for Education Statistics and is called SAT4. Please consider the difference (VA - MD). a) Define the parameter of interest in context using symbol(s) and words in one sentence. b) Obtain the value of the observed statistic used to estimate the parameter using StatKey or Rguroo. Upload your data set to either program to obtain your statistic and state the statistic rounded to one decimal place as your answer to this part. c) State the null and alternative hypotheses using correct notation. d) Create a bootstrap distribution. In StatKey, go to the middle pane labelled 'Bootstrap Confidence Interval' and click CI for Difference in Means. Upload the file in 'Upload File' or manually edit the data in 'Edit Data.' Click 'Generate 1000 Samples.' Click this button nine more times to obtain 10,000 samples. Copy your distribution in your solutions document. e) Construct a 99% confidence interval using percentiles. Go to the top left corner of the distribution and click 'Two-Tail' and then enter in the percentile values needed based on the significance level. Copy your distribution showing the confidence interval values into your solutions document. Also, provide your confidence interval in the format (lower value, upper value). f) Based on the confidence interval, provide a decision for the hypothesis test and explain your reasoning.e) Construct a 99% confidence interval using percentiles. Go to the top left corner of the distribution and click 'Two-Tail' and then enter in the percentile values needed based on the significance level. Copy your distribution showing the confidence interval values into your solutions document. Also, provide your confidence interval in the format (lower value, upper value). f) Based on the confidence interval, provide a decision for the hypothesis test and explain your reasoning. g) If we changed the significance level to 0.05 and constructed a 95% confidence interval, what would happen to the width confidence interval? In addition, explain if your decision from 4(f) changes if the significance level changes to 0.05. h) Create a randomization distribution. In StatKey, go to the right pane labeled Randomization Hypothesis Tests' and click 'Test for Difference in Means. ' Upload the file in 'Upload File' or manually edit the data in 'Edit Data.' Click 'Generate 1000 Samples.' Click this button nine more times to generate 10,000 samples. Take a screenshot of your randomization distribution and paste it into your solutions document. Part (i) is on the next page. 8i) Calculate the p-value from your randomization distribution using your observed statistic calculated in part 1(b). First, click the \"Right Tail' button and enter the value of your observed statistic in the blue box below the xaxis. Next, click the \"Left Tail' button and enter the negative value of your observed statistic the blue box below the xaxis (to the left of zero). Then, if necessary, readjust. your bottom blue box to the right of zero to con'ectly display the value of the observed statistic. Finally, add the values of the two blue boxes above their corresponding red x's to obtain the pvalue. Based on the pvalue found in 4(i), state whether you reject or do not reject the null hypothesis and a reason for your decision in one sentence. Based on the above decision, state your conclusion addressing the research question, in context. In general, explain 110w the bootstrap condence intewal and the randomization hypothesis test relate to one another in one to two sentences