Math
Math
Math
METHODOLOGY
CHAPTER III
THE RESEARCH METHODOLOGY
CONFIDENCE LEVEL
- precision rate – a percentage that can show how close you are to
the actual answer
- normally, we use 90%, 95% and 100% confidence level
- The Confidence Level is used to obtain a confident number of sa
mples from the population. These samples will then be subjected
to the different sampling techniques.
CONFIDENCE LEVEL AND
MARGIN OF ERROR
MARGIN OF ERROR
- error percentage that can show the maximum errors that your answer
can have
- normally, we use 0.1, 0.05, 0.01
- it gives you a space to commit error or it gives you an excuse to accept
that there is a different in results, especially in replicated studies.
EXAMPLE
𝑁 – population
LEGEND:
𝑒 – margin of error
𝑝 – sample proportion
𝑧 – standard score of level of confidence
(one-tailed)
[𝑁𝑧 2 ][𝑝 1 − 𝑝 ]
FORMULA 1: 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 =
𝑁𝑒 2 + 𝑧 2 [𝑝 1 − 𝑝 ]
𝑁
FORMULA 2: 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑖𝑧𝑒 =
1 + 𝑁𝑒 2
SAMPLE SIZE (POPULATION IS UNKNOWN)
σ– standard deviation
LEGEND:
𝑒 – margin of error
𝑝 – sample proportion
𝑧 – standard score of level of confidence
(one-teailed)
FORMULA 3: 𝒛×σ 𝟐
𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 =
𝒆
COFIDENCE LEVEL
The confidence level should be in standard score.
STEPS SOLUTION
[𝐍𝐳𝟐 ][𝐩 𝟏 − 𝐩 ]
2. IDENTIFY THE FORMULA TO USE. 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐢𝐳𝐞 =
𝐍𝐞𝟐 + 𝐳 𝟐 [𝐩 𝟏 − 𝐩 ]
95% / 2 = 47.5%
47.5% / 100 = 0.475
3. CALCULATE THE Z-SCORE.
STEPS SOLUTION
𝑵
2. IDENTIFY THE FORMULA TO USE. 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 = 𝟐
𝟏+𝑵 𝒆
(𝟏𝟎𝟎𝟎)
𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 = 𝟐
𝟏 + 𝟏𝟎𝟎𝟎 𝟎. 𝟎𝟏
(𝟏𝟎𝟎𝟎)
𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 =
3. SUBSTITUTE IN THE FORMULA AND COMPUTE 𝟏 + (𝟏𝟎𝟎𝟎)(𝟎. 𝟎𝟎𝟎𝟏)
(𝟏𝟎𝟎𝟎)
𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒊𝒛𝒆 =
𝟏 + 𝟎. 𝟏
𝟐
𝐳×𝛅
2. IDENTIFY THE FORMULA TO USE. 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐢𝐳𝐞 =
𝐞
95% / 2 = 47.5%
47.5% / 100 = 0.475
3. CALCULATE THE Z-SCORE.
The Standard Score is 1.96
In a certain village, Tzuyu wants to know how many people she can take as a sample but she
does not know the total population. She wants to be 95% confident and accepts 1% error. Assuming that from
a previous study, they used a standard deviation of 0.5 kg. How big is her sample size?
STEPS SOLUTION
𝟐 𝟐
𝟐 𝐬𝐚𝐦𝐩𝐥𝐞
𝟎. 𝟗𝟖 𝟏. 𝟗𝟔 × 𝟎. 𝟓
= 𝟗𝟖 𝐬𝐢𝐳𝐞 = 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐢𝐳𝐞 =
𝟎. 𝟎𝟏 𝟎. 𝟎𝟏
Mina wants to know the financial budget and the attitude of her
neighbors. she decides to pick the closest house to her because
she did not feel like going out on a very hot day. In the end, she
picked the houses near her.
NON-PROBABILITY EXAMPLE
KIND DEFINITION
SIMPLE RANDOM Relies on probability. Every individual has equal
SAMPLING chances