## 3 Written HomeworkSolve the following exercises. Upload your solution to Gradescope in PDF format. Show all the steps, not just the final answer. You need to show work when computing Binomial, Geometric, Poisson, Exponential, and Uniform probabilities. This means you cannot use special functions of your calculator to directly compute such probabilities. On any problem involving integrals, you cannot just use a calculator to get directly the solution. Instead, you need to solve the integral by hand and write down the steps.### Exercise 1:You are curious to know if UCSD students’ satisfaction with their college experience depends on whether they are living on campus or off campus. You interview 36 random UCSD students that live on campus and 40 random UCSD students that live off campus. You ask them to pick a number between 1 and 10 to evaluate their college experience. Below are the results:| | On campus | Off campus ||----------------|-----------|------------|| Mean | 7.5 | 7 || sd | 1.5 | 1.3 || N | 36 | 40 |a) Define the parameters of interest and the appropriate null and alternative hypotheses.b) State and check if the assumptions needed for conducting the appropriate hypothesis test are satisfied.c) Define the appropriate test statistic and calculate its value.

Parametric test are used to test the mean significance between sample and population. It follows the assumption of normal distribution. If we fails to assume the distribution then non parametric test is used. Each hypothesis test has two statements, they are null and alternate hypothesis. a) Given : Students satisfaction about their college changes whether they are on campus or off campus is studied. Parameter of interest : UCSD students satisfaction level about their college experience Null hypothesis : Students satisfaction about their college same for on campus or off campus experience i.e. H0 : μ1=μ2 Alternate hypothesis : Students satisfaction about their college different for on campus or off campus experience i.e. H1 : μ1≠μ2 b) Given : Assumption : 1. Here, two samples are independent. Since, on campus and off campus are taken from different people. 2. Two samples are taken from population. Since, both the sample taken from UCSD college. 3. Assume the population follows normal distribution Hence, all the assumptions for two independent sample t test is satisfied. c) Given : Test statistic : t=x¯1-x¯2n1-1s12+n2-1s22n1+n2-21n1+1n2=7.5-736-11.52+40-11.3236+40-2136+140=1.56 Test statistic is 1.56