Suppose that we have a political poll for voters' preference for the 2024 election. Suppose that Joe Biden will run for reelection, and he wants to assess his ability to defeat Donald Trump if he runs again in 2024 for a second term (as a historical note, there was only one US president, Grover Cleveland, who was elected president in two non-consecutive terms-winning in 1884, losing in 1888 to Benjamin Harrison, and then winning again in 1892). Suppose that you work for Joe Biden and want to create a poll to see how well Sanders will perform in Pennsylvania, which was an important state in the 2020 general election. Suppose that you want to create a confidence interval based on a SRS of 250 individuals, finding a sample proportion of p=0.57 that state that they would vote for Biden over Trump. Suppose we want to find a 95% CI for Joe Biden voters (for a 95% Cl, z* = 1.960). a.) Find the margin of error for your poll by hand (i.e. using the formula). b.) Calculate a 95% confidence interval for the proportion of Pennsylvania voters who will vote for Biden using Geogebre. Write down the Geogebra command you used and the confidence interval. c.) Suppose you want to test the claim that Biden will get a higher proportion of votes than Trump (in others, Biden will get more than 50% of the vote). Write down the null and alternative hypotheses below. d.) Complete the hypothesis test using Geogebra, Write down the Geogebra command you used below, and the corresponding P-value, using an a = 0.05 significance level. Then interpret the results of the test in terms of the original claim. Do you feel confident that Biden would defeat Trump in Pennsylvania based on this data?