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# Mathematics and Statistics : Statistics Assignment

Mathematics and Statistics : Statistics Assignment.

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Topic:

Any topic (writer’s choice)

Type of paper:

Statistics Assignment

Discipline:

Mathematics and Statistics : Statistics

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Pages: 2

Please see attached.  There is a word document and an excel spreadsheet attached.  I have also attached all the lectures where the answers for this assignment can be find.  This is NOT and essay.  You do not need any citations.

#### Module 6 Simple Random Sampling

1. Explain which elements in the sampling design process are informed by well written study objectives. (8 pts)

A well written study objective explains the study population from which the research will be conducted. Simply, the collection or objects from which the researcher derives information and makes reference is identified. The population defining terms including the elements, sampling units, extent and time can be derived from the objectives. Also, the sampling frame can be determined given the specifications in the objective. The population descriptive might imply the sampling frame from which population portion that the sample will be drawn.

• Explain what is missing from the following study objective statement (8 pts):

We wish to determine the total number of elk residing within Rocky Mountain National Park to within 15%.

Considering the population aspect, the element is elk, the sampling unit is elk residents in Rocky mountain national park, the extent is Rocky Mountain National Park, and the timeline is missing. The sampling frame would then be all residents of Rocky Mountain National Park.

• What is the definition of simple random sampling? Provide an example of how it can commonly be used. (6 pts)

Simple random sampling is a technique used to establish samples where all entities in the population have a known and equal likelihood of selection into the sample. The item selection is entirely dependent on its selection probability hence independent of likelihood of selecting any other items from the same population in the desired sample. It implies that if the population size is N and a sample of size n is desired then the probability of every item from the population to be selected into the sample will be n/N. Irrespective of the existing differences between the population elements each has an equal chance of selection. For instance, it can be applied in a research on a given animal species in a specified national reserve. A reserve can have over a thousand animals of the given species indicating that difficulties might be experienced in analyzing the desired input from the entire population. If a researcher wants a sample of 100 from the 1000, then each animal has a probability of 100/1000 = 0.1 to be selected; if n= 50, then the probability will be 50/1000 = 0.05.

• What are the differences between with and without replacement sampling and what do they mean for sample selection probability? (6 pts)

Simple random sampling is conducting using the two approaches; with and without replacement sampling. In the “with replacement” each item can be sampled as often as it is selected hence can be selected more than once as it is not removed from the population. In the “without replacement” each item can only be sampled once and it is removed from the population upon its selection. The items replacement or non-replacement from the population affects the sample selection probability. In the “with replacement” the selection probability remains constant all through but changes for those “without replacement.” Usually, after the selected item is removed from the population the number of the possible sample units decreases which increases the selection probability.

• When do we invoke the finite population correction factor and what is this doing when we utilize it? (6 pts)

The finite population correction factor is invoked when using the sampling without replacement approach and the sample population is small but the relative percentage to be measured starts to exceed 5%. The central limit theory might not hold or the standard error of the estimate might be too high. It is used to represent the population portion that will not be measured. When used, the estimated standard error is reduced given that the estimation does not include measured items.

• What assumptions can we make when we are using a sampling process with known relative probabilities and what does it mean for our statistical calculations? (6 pts)

The assumptions made are that the research estimator follows a normal distribution and the selection of the sample is random. The assumption facilitates easy computation of the standard error, and a better understanding and predictability of the rate at which the average of the sample approaches the population mean.

• From the following preliminary sample estimating the density of Artemisia spp. of shrubs per acre, determine how many samples are needed to estimate shrub density to within 12% at a 95% confidence level. Assume the population is infinitely large. (8 pts)

The sample size n should be 34 samples

• You are attempting to determine seedling density following a wildfire within a 60 acre stand, to design your study you install a set of 1/300th acre preliminary plots. From this data, determine how many 1/100th acre plots will be necessary to achieve a sample precision of 15% at a 90% confidence level? Be sure to determine if you need to account for the finite population correction factor. (10 pts)

For a precision of 15% at a 90% confidence level, 27 samples of 1/100th acre plots are necessary.

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