1.Let the expected distribution of students is as follows:

35% business, 28% engineering, 15% education, 12% nursing and 10% computer science.

We can set the null and research hypotheses as follows:

H0: The observed distribution of students is same as expected distribution

H1: The observed distribution of students is different from the expected distribution.

Chi-Square for Observed Counts in Variable No. of Students

Category Observed Frequency Historical Counts Test Proportion Expected Frequency Contribution to Chi-square

Business 84 35 0.35 82.60 0.02373

Engineering 68 28 0.28 66.08 0.05579

Education 42 15 0.15 35.40 1.23051

Nursing 27 12 0.12 28.32 0.06153

Computer

Science 15 10 0.10 23.60 3.13390

N DF Chi-Square P-Value

236 4 4.50545 0.342

2.Chi-Square for Observed Counts in Variable No. of Respondents

In this case, we can set the null and research hypotheses as follows:

H0: All colors have the same preference or each color has the probability 1/6.

H1: All colors have not the same preference or the probability of color is different than 1/6

Category Observed Test Proportion Expected Contribution to Chi-square

Black 32 0.166667 27 0.9259

White 53 0.166667 27 25.0370

Red 26 0.166667 27 0.0370

Green 20 0.166667 27 1.8148

Yellow 16 0.166667 27 4.4815

Blue 15 0.166667 27 5.3333

.

N DF Chi-Square P-Value

162 5 37.6296 0.000

Please explain clearly the data above and make a conclusion.