Simple Random Sampling | Contoh Acak Sederhana | contoh soal dan pembahasan

Summary

In this educational video, the instructor discusses a statistical problem involving simple random sampling to estimate the average annual spending of S1 Statistics students on dormitory rent in 2023. The video explains the process of calculating the sample mean, total expenditure for the entire population, and the bounds of error. The instructor also addresses how to adjust the sampling process for a population of 100 students in 2024, factoring in an 80% error margin from 2023. The video provides a clear step-by-step breakdown of the calculations and formulas used in this statistical analysis.

Takeaways

• 😀 The script discusses a statistical survey on the annual rental costs for dorm rooms for S1 statistics students in 2023.
• 😀 The survey sample consists of 12 respondents randomly selected from a population of 66 students.
• 😀 The main objective is to estimate the average annual expenditure for all students based on the sample data.
• 😀 To calculate the sample mean, the sum of all individual expenditures is divided by the sample size (n=12), resulting in an average of approximately 2.62 million IDR per year.
• 😀 The total expenditure for all 66 students is estimated by multiplying the average expenditure by the total population, resulting in around 172.7 million IDR per year.
• 😀 The Bound of Error is calculated using the formula 2 * sqrt(variance of the sample mean), leading to an error bound of approximately 0.4463 million IDR.
• 😀 The Bound of Error for 2024 is 80% of the Bound of Error from 2023, which is approximately 0.357 million IDR.
• 😀 The script uses variance from the 2023 sample to predict the required sample size for 2024, with a population of 100 students.
• 😀 The required sample size for 2024 is calculated to be 19 students to achieve a similar Bound of Error as in 2023.
• 😀 The script emphasizes the use of simple random sampling and highlights the lack of stratification or clustering in the survey design.

Q & A

What is the total number of students in the sample, and how many students were randomly selected?

The total number of students is 66, and 12 students were randomly selected for the survey.

What method of sampling was used in this survey, and why?

The method used is Simple Random Sampling, as the problem does not mention any stratification or clustering, only the sample size and population size.

How is the average expenditure for students calculated in the script?

The average expenditure is calculated by summing all the expenditures of the 12 students and dividing by 12 (the sample size). The result is 2.61667 million per year.

What is the total expenditure for all students, based on the sample data?

The total expenditure for all 66 students is approximately 172.7 million per year, calculated by multiplying the average expenditure (2.61667 million) by the total number of students (66).

What is the formula used to calculate the Bound of Error for the average expenditure?

The Bound of Error (B) is calculated using the formula: B = 2 * √(variance of the sample mean).

What is the estimated value for the Bound of Error in this example?

The Bound of Error for the average expenditure is approximately 0.45 million.

How is the Bound of Error for the 2024 survey calculated?

The Bound of Error for the 2024 survey is calculated by taking 80% of the Bound of Error from the 2023 survey. The value of 0.4463 is multiplied by 0.80 to get the result of 0.357.

What does the term 'n kecil' mean, and how is it used in the script?

'N kecil' refers to the sample size, which is 12 in this case. It is used in various calculations, including determining the Bound of Error and the variance of the sample mean.

Why is the population size in the 2024 survey 100 students, and how does it affect the sample size calculation?

The population size for 2024 is 100 students. This change in population size affects the sample size calculation, as the formula for determining the required sample size takes into account both the population size and the desired Bound of Error.

How many students should be surveyed in 2024 to achieve the same Bound of Error, and how is this calculated?

To achieve the same Bound of Error, approximately 19 students should be surveyed in 2024. This is calculated using the formula for sample size, which considers the desired error margin, the population size, and the estimated variance from the 2023 survey.