1. **Advantages and Disadvantages of Sampling Methods:** **Probability Sampling Methods:** - Simple Random Sampling: - Advantages: 1) Every member has an equal chance of selection. 2) Results are generalizable. - Disadvantages: 1) Requires complete population list. 2) Can be time-consuming for large populations. - Systematic Sampling: - Advantages: 1) Easy to implement. 2) Ensures evenly spread samples. - Disadvantages: 1) Can introduce bias if there's a pattern. 2) Not suitable if the population is ordered. - Stratified Sampling: - Advantages: 1) Ensures representation of subgroups. 2) Increases precision. - Disadvantages: 1) Complex to organize. 2) Requires knowledge of strata. - Cluster Sampling: - Advantages: 1) Cost-effective. 2) Useful for geographically dispersed populations. - Disadvantages: 1) Higher sampling error. 2) Less precise than other probability methods. **Non-Probability Sampling Methods:** - Convenience Sampling: - Advantages: 1) Easy and quick. 2) Inexpensive. - Disadvantages: 1) High bias. 2) Not representative. - Judgmental/Purposive Sampling: - Advantages: 1) Focused on relevant subjects. 2) Useful for expert opinions. - Disadvantages: 1) Subjective. 2) Limited generalizability. - Quota Sampling: - Advantages: 1) Ensures representation of characteristics. 2) Faster than stratified. - Disadvantages: 1) Potential selection bias. 2) Not truly random. - Snowball Sampling: - Advantages: 1) Useful for hard-to-reach populations. 2) Builds trust via referrals. - Disadvantages: 1) Bias towards connected participants. 2) Limits diversity. 2. **Recommendation:** For a four-campus university study, **Stratified Sampling** is recommended because it ensures representation from each campus (stratum), enhancing accuracy. 3. **Definitions:** - Confidence Level: The probability (expressed as a percentage, e.g., 95%) that the sample correctly reflects the population within the margin of error. - Margin of Error: The maximum expected difference between the true population parameter and the sample estimate. - Difference: Confidence level indicates the reliability of the estimate, while margin of error shows the precision. 4. **Sample Size Calculations:** Given: $N = 3475$, $Z = 1.96$ for 95% confidence, $E = 0.05$, $p = 0.5$ **a. Infinite Population Formula (Godden):** $$n_0 = \frac{Z^2 \times p \times (1-p)}{E^2}$$ Calculate: $$n_0 = \frac{1.96^2 \times 0.5 \times 0.5}{0.05^2} = \frac{3.8416 \times 0.25}{0.0025} = \frac{0.9604}{0.0025} = 384.16$$ Rounded sample size: $$n_0 = 384$$ **b. Finite Population Correction:** $$n = \frac{n_0}{1 + \frac{n_0 - 1}{N}} = \frac{384}{1 + \frac{384 - 1}{3475}} = \frac{384}{1 + \frac{383}{3475}} = \frac{384}{1 + 0.1102} = \frac{384}{1.1102} = 345.92$$ Rounded adjusted sample size: $$n = 346$$ **c. Yamane's Formula:** $$n = \frac{N}{1 + N e^2} = \frac{3475}{1 + 3475 \times 0.05^2} = \frac{3475}{1 + 3475 \times 0.0025} = \frac{3475}{1 + 8.6875} = \frac{3475}{9.6875} = 358.79$$ Rounded sample size: $$n = 359$$ **Summary:** - Infinite population formula sample size: 384 - Adjusted for finite population: 346 - Yamane's formula sample size: 359 **Academic honesty:** Calculations are based on established sampling formulas from statistical inference principles (e.g., Godden, Yamane).