Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
Margin of error: 0.06; confidence level 90% ^p and ^q unknown
n= (round up to the nearest integer)
Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is found using a z-table for 90% confidence, p = .5 (when value is unknown), q = 1 - p, ^2 means squared, * means to multiply, and E = .06.
Plug values into the formula and calculate n.
1033
To find the minimum sample size required to estimate a population proportion or percentage, we can use the following formula:
n = (Z² * p * q) / E²
Where:
- n is the sample size
- Z is the z-score corresponding to the desired confidence level
- p is the estimated proportion or percentage from previous data (unknown in this case)
- q is the complement of p (1 - p)
- E is the margin of error
In this case, the margin of error is 0.06, and the confidence level is 90%. Since both p and q are unknown, we will assume a worst-case scenario and use p = 0.5 (which maximizes the sample size).
First, we need to find the z-score for a 90% confidence level. The z-score can be found using a standard normal distribution table or a calculator. For a 90% confidence level, the z-score is approximately 1.645.
Now we can calculate the sample size:
n = (1.645² * 0.5 * 0.5) / (0.06²)
n = (2.706025 * 0.25) / 0.0036
n = 0.67650625 / 0.0036
n ≈ 187.363125
Since we need to round up to the nearest integer, the minimum sample size required to estimate the population proportion or percentage is approximately 188.
To find the minimum sample size required to estimate a population proportion or percentage, we need to use the formula:
𝑛 = (𝑧^2 * 𝑝̂ * 𝑞̂) / 𝐸^2
Where:
- 𝑛 represents the sample size.
- 𝑧 represents the z-score associated with the desired confidence level. For a 90% confidence level, the z-score is approximately 1.645.
- 𝑝̂ represents an estimation of the population proportion.
- 𝑞̂ represents 1 - 𝑝̂ (the complement of 𝑝̂).
- 𝐸 represents the margin of error.
As the given data indicates that ^p and ^q are unknown, we can use a worst-case scenario approach. In this case, we assume that ^p = ^q = 0.5.
Substituting the given values into the formula:
𝑛 = (1.645^2 * 0.5 * 0.5) / 0.06^2
𝑛 = (2.706 * 0.25) / 0.0036
𝑛 = 0.6765 / 0.0036
𝑛 ≈ 187.36
Rounding up to the nearest integer, the minimum sample size required to estimate a population proportion or percentage is 188.