Investigation 2: FirstGeneration College Students Universities across the country are building aggressive recruitment and outreach programs designed to identify, support, and encourage prospective underserved and underrepresented students to apply. A common underserved and underrepresented group are rstgeneration students, dened as individuals who are the rst in their families to attend college. In August 2021, a higher education administrator was interested in comparing George Mason University and University of Virginia's percentage of rst- generation students accepted in their freshman classes for Fall 2021. From a random sample of 167 Mason freshman, 34 were rstgeneration students. From a random sample of 145 UVA freshmen, 16 were rstgeneration students. a) What is the parameter of interest? Use words and a symb01(s) in context in your answer. Dene any subscripts that you use. Calculate and label the two sample proportions separately and round each value to four decimal places. Next, calculate the difference between these sample proportions of George Mason University and University of Virginia by subtracting (Mason UVA). Type these calculations by hand, label each of them, and present each of these values in your solutions document. Create a bootstrap distribution. In StatKey under the middle pane labeled 'Bootstrap Condence Intervals', click CIfor Difference in Proportions. Click 'Edit Data', then enter in the count and sample size for each group. Make Group 1 Mason and Group 2 UVA. Next, click 'Generate 1000 Samples.' Take a screenshot of your bootstrap distribution including the mean and stande error and paste it in your solutions document. Describe the shape of the bootstrap distribution. Construct a 95% bootstrap condence interval using the J_r 28E method. Show all work and present your answer as (lower value, upper value). Interpret the meaning of the condence interval in context. UVA. Next, CHICK Generale 1000 Samples. Take a screenshot of your bootstrap distribution including the mean and standard error and paste it in your solutions document. d) Describe the shape of the bootstrap distribution. e) Construct a 95% bootstrap confidence interval using the + 2SE method. Show all work and present your answer as (lower value, upper value). f) Interpret the meaning of the confidence interval in context. g) Does your 95% confidence interval capture 0? Based on your answer, can we infer anything about whether a difference exists between the universities? Answer these questions in the context of the problem in one or two sentences. h) Construct a 99% confidence interval using the percentile method in StatKey. 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. Present a screenshot of your bootstrap distribution (with the blue boxes visible) and write your answer as (lower value, upper value).Interval tab and choose bootstrap (Percentile) under method. Finally, edit the Condence Level appropriately to generate both condence intervals. Copy and paste only the output and table displayed under the title \"Condence Interval for the Difference of Two Population Proportions\" for both the 95% and the 99% condence interval. If the administrator was testing the hypothesis that there exists a difference between the proportion of rst- generation students at Mason and UVA, state the null and alternative hypotheses using correct notation. Consider Mason as Population 1 and UVA as Population '2. Create a randomization distribution. In StatKelt-i, go to the right pane labeled 'Randonlization Hypothesis Tests' and click Testfor Dt'erence in Proportions. Edit the data in 'Edit Data.\" and click 'Generate 1000 Samples.' Screenshot your distribution and paste it in your solutions document. m) Why is your randomization distribution centered at zero? Answer in one sentence. n) Calculate the pvalue from your randomization distribution using your observed statistic calculated in part l(b). First, click the \"Right Tail' button and enter the value of your observed statistic in the blue box below the x-axis. 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 correctly 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. Is this p-value signicant at the 5% signicance level'? Is it signicant at the 1% signicance level? Compare the answers to these questions to your answers to parts (g) and (ii) in two complete sentences. Can we generalize these results to a larger group (i.e. a population)? Answer this question in one sentence and please provide a reason in your