Certainty independent of credits earned

Solution Preview

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Null hypothesis: There is no relationship between credits and choice of major.
Alternative hypothesis: There is a relationship between credits and choice of major.

Level of significance alpha 0.01

Observed frequency
Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0-9 12 8 3 23
10-59 8 4 10 22
60 or more 1 7 11 19
Column Total 21 19 24 64

Expected frequency
Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total
0-9 7.5 6.8 8.6 23
10-59 7.2 6.5 8.3 22
60 or more 6.2 5.6 7.1 19
Column Total 21 19 24 64

Expected frequencies for contingency table under the assumption of independence

For example

Similarly the expected frequencies for all other frequencies can be calculated.

Test Statistics:

Where o ij is the observed frequencies and the e ij is the expected frequencies

Table for computing the test statistics:

Observed Expected (O-E) (O-E)^2 ((O-E)^2)/E
12 7.5 4.5 20.25 2.7
8 6.8 1.2 1.44 0.211765
3 8.6 -5.6 31.36 3.646512
8 7.2 0.8 0.64 0.088889
4 6.5 -2.5 6.25 0.961538
10 8.3 1.7 2.89 0.348193
1 6.2 -5.2 27.04 4.36129
7 5.6 1.4 1.96 0.35
11 7.1 3.9 15.21 2.142254
Chi square 14.8104

From the table we have the calculated chi square value to be 14.8104
Critical value
With the (r-1)*(c-1)= (3-1)*(3-1)= 4 degrees of degrees of freedom and at 0.01 level of significance the critical value of the chi square is 13.277

Conclusion:

Since the calculated chi-square value is greater than the critical value the null hypothesis is reject. There is a relationship between credits and choice of major.

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