A college conducts an evaluation of student performance and departmental efficiency.
Part A: Single Mean (t-test)
The college claims that the average marks of students in Statistics is 75.
A sample of 16 students shows:
- Sample mean = 72
- Sample standard deviation = 8
Part B: Two Sample Means (t-test)
Two departments are compared:
- Department A: nᐁ = 12, mean = 78, variance = 25
- Department B: nᐂ = 10, mean = 72, variance = 36
Part C: Chi-square Test
The distribution of students᎙ grades is observed:
| Grade | Observed Frequency |
|---|---|
| A | 18 |
| B | 22 |
| C | 10 |
| D | 5 |
Expected distribution (theoretical):
A: 20%, B: 30%, C: 30%, D: 20% of 55 students.
Part D: F-test (Variance Comparison)
Two machines used for evaluation marking show variability:
- Machine 1: variance = 64
- Machine 2: variance = 36
t-test for Single Mean
a) State the Null and Alternative Hypotheses.
b) Write the formula for t-test.
c) Test whether the population mean is 75 at 5% level of significance (df = 15).
d) Interpret the result in academic context.