Practice Final 5 Problem 4. Inference for proportions The Department of Statistics estimates that 50% of students at the University of Washington will have taken STAT 311 by the time they graduate. You believe it is less than 50%, and decide to take a survey of graduating seniors to estimate the true proportion. Your friend gets you a list of the graduating seniors and their email addresses, and you randomly select a sample of n=200, email them, and ask them to report on a Catalyst survey whether they have taken STAT 311: 40% of seniors report that they have. Set up a 90% CI for the estimated proportion of seniors who have taken STAT 311. 4.1Symbolic representation: ?̂ ± ?𝛼/2∗ √?̂ (1−?̂)?or ? = ± ?𝛼/2∗ √?̂ (1−?̂)?4.2With plug-in values: 0.40 ± 1.64 ∗ √0.4(1−0.4)200= 0.40 ± 0.06 or [0.34, 0.46]State the null and the general alternative hypotheses. What is the approximate distribution of the sample proportion under the null hypothesis?