Discuss two reasons why researchers tend to work with samples instead of populat

Question

Discuss two reasons why researchers tend to work with samples instead of populations?

What is the definition of random sampling and what are its advantages?

Find the standard error of the mean if the following sample is drawn from a population with a standard deviation of 1.50:

7.00, 8.00, 9.00, 12.00, 11.00, 8.00, 10.00, 9.00, 9.00

Find the standard error of the mean if the following sample is drawn from a population with a standard deviation of 4.50:

24.00, 23.00, 21.00, 24.00, 24.00, 25.00, 23.00, 23.00, 26.00

What is the Central Limit Theorem and what does it state about the sampling distribution of X-Bar?

Explanation / Answer

The reasons why researchers tend to work with the sample are :

1. Reduced complexity as it is easier to deal with a sample of the population rather than the whole population

2. It is easier to collect relevant data for the sample compared to the population so sampling reduces cost and time.

Random sampling is when various samples from the poulation are selected at random, i.e. not in any order. The sample size of various samples chosen may even be different.

The advantage of using it is the ease of use as we work with a smaller dataset and it is a true representation of the entire population as the samples are taken at random.

n = 9, sigma = 1.5

So, std error of mean = sigma/sqrt(n) = 1.5/sqrt(9) = 1.5/3 = 0.5

n = 9, sigma = 4.5

So, std error of mean = sigma/sqrt(n) = 4.5/sqrt(9) = 4.5/3 = 1.5

The Central Limit Theorem states that for sufficiently large samples taken from the population and having finite variance, the distribution that the sample follows would be normal with mean equal to population mean and standard deviation equal to population standard deviation divided by square root of the sample size.

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