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Unit 6: Sample Size Determination - Coggle Diagram
Unit 6: Sample Size Determination
Normal Distribution
Characteristics: mean = median = mode, symmetry about the center, 50% of values less than and greater than the mean.
Understanding Standard Deviation
: It is crucial because it allows us to say that any value is:
Likely within 1 SD (68 out of 100 should be).
Very likely within 2 SDs (95 out of 100 should be).
Almost certainly within 3 SDs (99.7 out of 100 should be).
Example: Student heights between 1.1m and 1.7m; Mean = 1.4m; SD = 0.15m.
Z-Score Example
Friend's height: 1.85m is 3 SDs from the mean of 1.4m, giving a Z-score of 3.0.
What is a Z-Score
: The number of standard deviations a data point is from the mean. Calculated as (Value - Mean) / SD.
Standardizing Process
:
Value → Subtract Mean → Divide by SD → Z-Score.
Sampling Distribution of Mean
According to the Central Limit Theorem, arithmetic means of large random samples will form a normal distribution curve, matching the population mean.
Standard Error Formula
Format: Sample mean, Frequency, Deviation from assumed mean (d), d/0.5, fd, d², fd².
This format helps in the calculation of mean and standard deviation.
Important Terms
Parameter
: A fixed characteristic or measure of the target population.
Statistic
: A characteristic or measure of the sample.
Finite Population Correction (fpc)
: Corrects overestimation for sample sizes ≥ 5% of the population.
Sample Size Determination
Considerations: Allowed error, desired confidence level, estimated population SD.
Formula
Determining Sample Size with Known Standard Deviation
Examples of determining the necessary sample size for estimating average amounts per invoice in populations of sales invoices with specified SDs and allowable errors.
Stratified Sample Size
Comparing proportionate vs. disproportionate stratified sample sizes for market research in luxury retail.
Stratified Sampling Process
:
Identify Strata → Determine SD and Size per Stratum → Calculate Sample Size.
Formula
Sample Mean Frequency Format
Format: Sample mean, Frequency, Deviation from assumed mean (d), d/0.5, fd, d², fd².
This format helps in the calculation of mean and standard deviation.