At a college, 29% of the students are in their first year, 27% are in their seco

Question

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 1st 2nd 3rd 4th Total College Percents 29% 27% 25% 19% Sample Counts 49% 70% 56% 25% Total Sample Counts 200 Expected Counts 58(1) 54(2) 50(3) 38(4) Under the assumption that we think the college enrollment percents should match our sample, and that therefore our sample represents the college: a) What would the critical value be? (use = 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?

Explanation / Answer

a) here degree of freedom =(number of categories-1) =4-1=3

therefore for 3 degrees of freedom and 0.05 level; critical value =7.815

b)

from above test stat X2=11.305

c)as test stat is higher then critical value at = 0.05, we   reject that sample represent the college

observed Expected Chi square Probability O E=total*p =(O-E)^2/E first year 0.290 49.000 58.00 1.40 second year 0.270 70.000 54.00 4.74 third year 0.250 56.000 50.00 0.72 fourth year 0.190 25.000 38.00 4.45 1 200 200 11.3047

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