Contents
How do you estimate the total population?
The population size estimate is obtained by dividing the number of individuals receiving a service or the number of unique objects distributed (M) by the proportion of individuals in a representative survey who report receipt of the service or object (P).
How do you find the total number of sample values?
Estimating a Population Total
- Sample mean = x = Σx / n.
- Population total = t = Nx.
- where N is the number of observations in the population, and x is the sample mean.
- s2 = Σ ( xi – x )2 / ( n – 1 )
What is sample size needed to estimate the population total, τ?
What sample size is needed to estimate the population total, τ, to within d = 1000 with a 95% CI? Now, let’s begin plugging what we know into the formula. We know N = 100, α = 0.05. Do we know σ 2? No, but we can estimate σ 2 by s 2 = 1932.657. How many should we sample? Let’s calculate this out and:
How to calculate the confidence interval for a population mean?
If we want to estimate µ, a population mean, we want to calculate a confidence interval. The 95% confidence interval is: ¯x ±2 σ √n x ¯ ± 2 σ n. We can use this formula only if a normal model is a good fit for the sampling distribution of sample means. If the sample size is large ( n > 30), we can use a normal model.
Why is there an error in estimating the population mean?
The error is due to random chance. Likewise, a sample mean is an estimate for the population mean, but there will be some error due to random chance. Recall that, in Inference for One Proportion, we adjusted the standard error by replacing p with the sample proportion.
Can you use this formula to estimate the sample size?
Now, if we specify 1 − α , the margin of error d (also can be viewed as the half width of the ( 1 − α) 100% CI), we can solve for the sample size such that the CI has the specified margin of error. Can we now use this formula to estimate the sample size? What is the weak point of this formula?