One Sample Z-Interval for Population Proportion INTERVAL
1. Random sample or assignment2. 10% Condition n ≤ 1/10(N)3. a) Population distribution is stated as NORMAL b) n ≥ 30 c) if n < 30, check graph of sample data to verify no strong skew or outliers
A one sample Z-interval for population proportion is a statistic used to estimate the true proportion of a characteristic in a population, based on a sample of data. It determines the range of values within which the true proportion is likely to lie.
To calculate a one sample Z-interval for population proportion, the following steps should be taken:
1. Collect a random sample of data from the population of interest.
2. Determine the sample proportion (p) by dividing the number of observations with the characteristic of interest by the total sample size.
3. Determine the standard error of the sample proportion using the formula:
SE = √(p(1-p)/n)
where n is the sample size.
4. Determine the critical value of the standard normal distribution for the desired level of confidence (usually 95% or 99%).
5. Calculate the margin of error using the formula:
E = Z*SE
6. Determine the lower and upper bounds of the confidence interval using the formulas:
Lower bound = p – E
Upper bound = p + E
The resulting interval provides a range of values for the true population proportion with a certain level of confidence.
It is important to note that this method assumes that the sample is random, independent, and representative of the population. If any of these assumptions are violated, the resulting interval may not be accurate in estimating the population proportion.
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