Practice Final5Problem 4.Inference for proportionsThe Department of Statistics estimates that 50% of students at the University of Washington will have takenSTAT 311 by the time they graduate.You believe it is less than 50%, and decide to take a survey of graduatingseniors to estimate the true proportion.Your friend gets you a list of the graduating seniors and their emailaddresses, and you randomly select a sample of n=200, email them, and ask them to report on a Catalystsurvey 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 sampleproportion under the null hypothesis?