Investigation 3: 2021 Virginia Math SAT Scores In 2021, a sample of 400 high school seniors was randomly selected from Virginia (VA) and each of their math SAT scores was recorded. The US. average for the math section on the 2021 SAT was 528 (out of a total of 800). We would like to know if Virginia high school seniors scored better than the average US. high school senior at the 5% signicance level. This data comes from the National Center for Education Statistics and is called SA T3. a) Dene the parameter of interest in context using symbol(s) and words in one complete sentence. State the null and alternative hypotheses using correct notation. State the observed statistic from the sample data we will use to complete this test. Create a randomization distribution. In StatKev, go to the right pane labeled 'Randomization Hypothesis Tests' and click Testfor Single Mean. Upload the le in 'Upload File' or manually edit the data in \"Edit Data.' Change the 'Null hypothesis: u\" to the mean you stated in your null hypothesis. Next, click 'Generate 1000 Samples.' Screenshot your entire randomization distribution and paste it into your solutions document. Describe the shape of the distribution. Based on your answer, are we able to continue with a randomized hypothesis test? Answer in one sentence. Regardless of your answer in 3(e), calculate the pValue of this test. To nd the pvalue from the randomization distribution click either 'Left Tail\State the observed statistic from the sample data we will use to complete this test. Create a randomization distribution. In Sthey, go to the right pane labeled 'Randomization Hypothesis Tests' and click Testfor Sir-1312 M'ecm. Upload the le in 'Upload File' or manually edit the data in \"Edit Data.' Change the 'Null hypothesis: u\" to the mean you stated in your null hypothesis. Next, click 'Generate 1000 Samples.\" Screenshot your entire randomization distribution and paste it into your solutions document. Describe the shape of the distribution. Based on your answer, are we able to continue with a randomized hypothesis test? Answer in one sentence. Regardless of your answer in 3(6), calculate the pvalue of this test. To nd the pvalue from the randomization distribution click either 'Left Tail\