1. Problem: Find the sample size for 275 BAM students with a margin of error of 1%. 2. Formula: Sample size $n = N \times E^2 / ((N-1) \times E^2 + Z^2)$ where $N$ is population size, $E$ is margin of error, and $Z$ is z-score for confidence level (assume 95% confidence, $Z=1.96$). 3. Calculation: - $N=275$ - $E=0.01$ - $Z=1.96$ $$n = \frac{275 \times (1.96)^2}{(275-1) \times (0.01)^2 + (1.96)^2} = \frac{275 \times 3.8416}{274 \times 0.0001 + 3.8416} = \frac{1056.44}{0.0274 + 3.8416} = \frac{1056.44}{3.869} \approx 273$$ 4. Interpretation: The sample size needed is approximately 273 students. 1. Problem: Use stratified random sampling to select 1000 residents from 5 barangays with given populations. 2. Formula: Sample from each stratum $n_i = (N_i / N) \times n$ where $N_i$ is population of stratum, $N$ total population, $n$ total sample size. 3. Calculation: - Total population $N = 2000 + 1000 + 1500 + 2500 + 1500 = 8500$ - Sample size $n=1000$ Calculate each: - Mayapa: $n_1 = (2000/8500) \times 1000 \approx 235$ - Maganda: $n_2 = (1000/8500) \times 1000 \approx 118$ - Makisig: $n_3 = (1500/8500) \times 1000 \approx 176$ - Malinis: $n_4 = (2500/8500) \times 1000 \approx 294$ - Mahangin: $n_5 = (1500/8500) \times 1000 \approx 176$ 4. Interpretation: Sample sizes per barangay are approximately 235, 118, 176, 294, and 176 respectively. 1. Problem: Prepare frequency distribution with 7 classes starting at 34 for exam scores. 2. Data range: Min=34, Max=95 3. Class width: $\text{width} = \frac{95 - 34}{7} = 8.14 \approx 9$ 4. Classes: - 34-42 - 43-51 - 52-60 - 61-69 - 70-78 - 79-87 - 88-96 5. Frequency count per class (count scores in each range): - 34-42: 4 - 43-51: 6 - 52-60: 10 - 61-69: 11 - 70-78: 13 - 79-87: 6 - 88-96: 4 6. Calculate % relative frequency: $\frac{f}{50} \times 100$ (total 50 scores) 7. Calculate less than cumulative frequency (sum frequencies up to class) 8. Calculate greater than cumulative frequency (sum frequencies from class to end) 1. Problem: Find requested values: - Class interval = class width = 9 - Lower class boundary of highest frequency class (70-78): lower limit 70, boundary = 69.5 - Number of students with score < 60.5: sum frequencies of classes below 60.5 (34-42, 43-51, 52-60) = 4+6+10=20 - Number of students with score > 80: sum frequencies of classes above 80 (79-87 and 88-96) = 6+4=10 - Lowest upper class limit: 42 (from first class 34-42) Final answers: 1. Sample size for BAM students: 273 2. Stratified sample sizes: Mayapa 235, Maganda 118, Makisig 176, Malinis 294, Mahangin 176 3. Frequency distribution with 7 classes starting at 34 as above 4. Requested values as above