QUESTION 21 Suppose we know that at a University XYZ that 30% of students receiv

Question

QUESTION 21 Suppose we know that at a University XYZ that 30% of students receive an A in their introductory statistics class, 30% receive a B, 20% receive a C. 10% receive a D. and 10% receive an F. For comparison, a sample of 300 students at University ABC is taken and 20% received an A 28% received a B. 26% received a C. 15% received a D. and the remaining students failed the class. When testing (at the 5% level of significance) whether the proportions between the two universities are different. what is the null and altemative hypotheses? (please write out the null and alternative hypotheses below AND on your scratch work failure to do BOTH will result in 0 points) v 3 (12pt) 6 pr

Explanation / Answer

H0: There is no significance difference between the proporiton of two universities

H1: There is significance difference between the proporiton of two universities

Let the los be alpha = 5% = 0.05

The observed frequencies are calculated as Ratios*300 similiarly expected frequencies also.

From the given data,

Num Categories: 5

Degrees of freedom: 4

Using chisquare distribution,

Test Statistic, X^2 = 23.6000
Critical X^2: 9.48772
P-Value: 0.0001

Here P-value < alpha 0.05 and also chisquare value = 23.6 > critical value of chisquare 9.4877, So we reject Ho

Thus, we conclude that there is significance difference between the proporiton of two universities

Observed Observed Expected Expcted Ratios freq (Oi) Ratios freq (Ei) (Oi-Ei)^2 / Ei A 0.20 60 0.30 90 10 B 0.28 84 0.30 90 0.4 C 0.26 78 0.20 60 5.4 D 0.15 45 0.10 30 7.5 Failed 0.11 33 0.10 30 0.3 Total: 23.6

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