Question

1.Suppose that the percentage distribution of U. S. college students’ classes as Freshmen, Sophomores, Juniors, Seniors, Graduate and Post Graduate has been established by the 2020 census. Suppose we took a random sample of 1,000 students from the University of Alaska Anchorage in 2020 and found the following distribution to be:

CLASS % DISTRIBUTION STUDENTS

Freshmen	15	180
Sophomores	10	260
Juniors	25	210
Seniors	30	150
Graduate	15	100
Post Graduate	5	100
Total:	100%	1,000

On the basis of the sample evidence, could we conclude that the University of Alaska Anchorage, fits into the distribution of the CY 2010 census data or has the University applied special emphasis in some category of students? Utilize the Chi-Square distribution, testing the Null Hypothesis with a ten percent significance level. please show all work

Answer 1

Ho : the University of Alaska Anchorage, fits into the distribution of the CY 2010 census data

H1 : the University of Alaska Anchorage, does not fits into the distribution of the CY 2010 census data

Here 0 p 0.15 n= 6 E = p*1000 (0-E) (0-E)?/E 150 30 6 180 0.1 260 100 160 256 0.25 210 250 -40 6.4 0.3 150 300 -150 75 0.15 100 150 -50 16.667 0.05 100 50 50 50 Total 1000 1000 410.07 The test statistic is (0-E x2 = E 410.067 Degrees of freedom = 6-1 = 5 P-value = 0 [using Excel function CHIDIST(410.067,5)] Decision rule : Reject H0 if P-value <a Here P-value = 0 < 0.1 = a. Conclusion: By decision rule, we reject HO