This semester, we have talked about creating random samples as well as desirable qualities of random samples. Other than randomness, one quality of random samples that we have talked about is representation. Using your knowledge of that concept, consider this problem.At a college, 29% of the students are in their first year, 27% are in their second year, 25% in their third, and 19% in their fourth. You take a survey of students and when you classify them by year of study, you have 49, 70, 56, and 25 students in their first, second, third, and fourth years respectively.The table below highlights this information:| Year of School | First | Second | Third | Fourth | Total ||----------------|-------|--------|-------|--------|-------|| College Percents | 29% | 27% | 25% | 19% | || Sample Counts | 49 | 70 | 56 | 25 | 200 || Expected Counts | 58 | 54 | 50 | 38 | |Under the assumption that we think the college enrollment percentages should match our sample, and that therefore our sample represents the college:a) What would the critical value be? (use α = 0.05)b) Find the test statistic to test (c) above.c) Based on your answers above, does your sample appear to represent the college?

The table shows the college percent's, sample counts and expected counts for year of school (First, second, third, and fourth).a) The degrees of freedom is, df=k-1=4-1=3 The critical value of chi-distribution for 0.05 level of significance at 3 degrees of freedom with 0.10 can be obtained using the excel formula “=CHISQ.INV.RT(0.05, 3)”. The critical value is 7.815. Therefore, the critical value is 7.815.b) The test statistic is, χ2=∑Observed-Expected2Expected=49-58258+70-54254+56-50250+25-38238=1.397+4.741+0.72+4.447=11.305 Therefore, the test statistic is 11.305.c) Decision rule: If the test statistic greater than critical value, then reject the null hypothesis (The college enrollment percentages should match our sample). Conclusion: The test statistic is greater than critical value. Based on the decision rule, fail to reject the null hypothesis. The college enrollment percentages should not match our sample. Therefore, the sample does not appear to represent the college.