Question

In: Math

2. A University has completed an internal survey on its department achievements. The key question in...

2. A University has completed an internal survey on its department achievements. The key question in the survey is whether the professors think the new on-line system is effective. The following is the output of a statistical analysis of the data:

Is online system effective

Purpose

No

Yes

Assignments

30

35

Labs and hand on activities

25

40

Exams

20

45

Based on this output, can the president conclude that the opinion of the professors on whether the recently launched on-line system is effective is dependent on which region they belong to? Use a chi square test and a level of significance of 0.05.

answer in word only pls

Expert Solution

given that

	Assignments	Labs and hand on activities	Exams	Total
No	30	25	20	75(r1)
Yes	35	40	45	120(r2)
Total	65(c1)	65(c2)	65(c3)	195

we need to test that Yes or no depends on the region or not

for that we will use chi square test

for that first we need to find the expected frequency for each cell

which is calculated as follows

the expected frequency for cell (i,j) is calculated as follows

where i=1,2 j=1,2,3

for example for cell (1,1) expected frequency is given by

similarly, for others values are given in the table

	assignments	Labs and hand on activities	exams	total
No	25	25	25	75
yes	40	40	40	120
	65	65	65	195

Now chi square value is given by

where

obsf(i,j) is observed value of cell (i,j)

while expf(i,j) is expected value of cell (i,j)

Now df of chi square =(r-1)(c-1) =(2-1)*(3-1) =2 where r= no.of rows c=no.of columns hence

since P-Value is higher than level of significance hence we failed to reject the null hypothesis

hence new online system effectiveness is not depend on the region

milcah answered 1 year ago

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