(5) In a random sample of 41 students from our opening week survey, there were 15 business null ors. (a) Determine a confidence interval for the proportion of all Math 37 students who are business majors. (b) HOW many students should have sampled if wanted to guarantee a margin Of error of at most 0.1 using a confidence level? (c) Perform a hypothesis test to determine if the proportion of busines students in Math 37 is significantly different from 0.5. Use a 0.05 significancy level for the test. (6) The following table summarizes the previous semester gpa of a random sample of II Students from our opening work Survey based Ot. Whether preferred online uvre neutral, or preferred in Group Sample Size [n person Neutral Online 27 Mean 2.94 322 3.36 SD 0.98 0.54 0.36 (a) State the null and alternative hypothcis for a test to determine if there is a signifi- cant difference in mean GPAs between grou1W (b) Calculate the mean squared error (MSE) for this data. (c) According to R, the "-value for this test was 0.29. If use a 0.1 significance level, what should be the conclusion of our test? (7) table below Status Of titanic based on their CIEL* First Died Survived 67 47 63 (a) What is the probability that a randomly selected passenger survived given that they v.en in the first class? (b) How many first class passengers would have expected to survive if class and survival status were independent? (c) What is the chi-square component for first chess, surviving passengers? (d) The total chi-square value for the table above is Use this number to perform hypothesis test to determine if class and survival status were independent. Use a 0.01 significance level for the te-t.