Can someone please help solve this problem.? al. 1980; for moose see Bartmann et
ID: 3303889 • Letter: C
Question
Can someone please help solve this problem.? al. 1980; for moose see Bartmann et al. 1987) Now you do it! 1. Let's say we know how many greater short-horned lizards are in our sampling frame (see Figure 4). (A sampling frame is a complete list or mapping of sampling units.) We can se that p 0.27 (ie, 27 plots-or 27% of the plots-contain at least 1 lizard) and N-336 th ere are 33 lizards in our sampling frame in Figure 4). In real-world situations, we obviously would not have this information. So how do we assess the quality (i.e, accuracy and precision) of our population estimates when we do not know the actual population size?Explanation / Answer
In this problem, we have been provided with information about the sampling frame (or population, as we commonly call it). It is given that the probability of finding a lizard p = 0.27 and the number of plots containing lizards = 33 (out of 100).
Now, there may be cases when we don't now or are unsure about the population size. We can then assess the quality (accuracy and precision) of our population estimates. For this, though, we need to select a suitable sample size first.
It becomes problemmatic to decide on the sample size if population size is unknown, but using the formula which I will state below, one can decide on the sample size and by setting a suitable confidence level, one will be able to assess the accuracy and precision of the population estimate.
Margin of Error (Confidence Interval) — No sample will be perfect, so we need to decide how much error to allow. The confidence interval determines how much higher or lower than the population mean we are willing to let our population estimate fall.
Confidence Level — How confident do we want to be that the actual population parameter value falls within our confidence interval? The most common confidence intervals are 90% confident, 95% confident, and 99% confident.
Standard of Deviation — How much variance do we expect in your responses? Since we haven’t actually administered our survey yet, the safe decision is to use .5 – this is the most forgiving number and ensures that our sample will be large enough.
Now that we have these values defined, we can calculate our needed sample size.
Our confidence level corresponds to a Z-score. This is a constant value needed for this equation.
The Z-scores for the most common confidence levels:
• 90% – Z Score = 1.645
• 95% – Z Score = 1.96
• 99% – Z Score = 2.326
If we choose a different confidence level, we use the Z-score table above to find our score.
Next, we use the following equation to determine sample size:
Necessary Sample Size = (Z-score)² * StdDev*(1-StdDev) / (margin of error)²
(Note: In some cases, one can replace StdDev by the "probability of picking a choice or response" or "population proportion", if known)
Here, assuming we chose a 95% confidence level, margin of error becomes 5% or 0.05. Likewise for 99% confidence level, margin of error is 0.01.
If we find our sample size too large to handle, we try slightly decreasing our confidence level or increasing our margin of error – this will increase the chance for error in your sampling, but it can greatly decrease the sample size we need.
Now, sampling accuracy is usually expressed as a relative index in percentage form and indicates the closeness of a sample-based parameter estimator to the true population value. When sample size increases and samples are representative, sampling accuracy also increases. Its rate of growth, very sharp in the region of small samples, becomes slower beyond a certain sample size.
Population estimates can be of high precision (that is with narrow confidence limits), but of low accuracy. This occurs when samples are not representative and the resulting estimates are lower or higher than the true data population value. When sample size increases precision also increases as a result of decreasing variability.
So, all in all, in order to achieve a good accuracy and precision level, we need to select a substantially large and representative sample (the sample size being determined by the formula provided). Confidence level can be kept at 95% and the margin of error at 5%, so that we obtain an optimal sample size. Selection of huge sample sizes is not feasible and recommended, though, because beyond a certain sample size the gains in accuracy are negligible, while sampling costs increase significantly.