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27. (6 points total) Test whether there is a difference between two groups in the proportion who voted, if 45 out of a random sample of 70 in Group 1 voted and 56 out of a random sample of 101 in Group 2 voted. a. (2 points) Find the relevant sample proportions in each group and the pooled proportion. (Round your answers to three decimal places) b. (2 points) State the null and alternative hypotheses. c. (2 points) Give the test statistic and the [J-value. Round your answer for the test statistic to two decimal places and your answer for the []-value to three decimal places. 28. (6 points total) Pennsylvania Seniors Favorite Subject? Exercise 1.24 describes a dataset, stored in PASeniors, for a sample of 457 Pennsylvania high school seniors who did the Census at School project. The data contain responses from the decade 2010-2019. One of the questions asks about favorite school subject. We see that 39 out of 186 students fromthe first half of the decade (2010-2014) chose “mathematics and statistics,” while 69 out of 268 students in the second half of the decade (2015-2019) made this choice. (Three students did not answer this question.) Does this provide enough evidence that the proportion of students picking mathematics and statistics as a favorite subject has changed between the first and second halves of the decade? (Let Group 1 represent the first half of the decade and Group 2 represent the second half of the decade.) a. (2 points) State the hypotheses. b. (2 points) Find test statistic and p-value. Round to three decimal places. c. (2 points) What do you conclude? 29.(3 points) Use the formula to find the standard error of the distribution of differences in sample means: Samples of size 45 from Population 1 with mean 3.2 and standard deviation 1.9 and samples of size 45 from Population 2 with mean 2.8 and standard deviation 1.1