Question

A. A survey of 20 Australian companies indicated that the average annual income of company secretaries was $120000. Assuming that the population standard deviation is $7500 and that the annual incomes are normally distributed. On the basis of above example. In your own word, explain the terms below. Where possible, also give an example from the newspaper article above:​(5x1 = 5 marks)

i. Significance level​​​​​​

ii. Sampling distribution.​

iii. Point estimator​​​​​​​​

iv. Margin of error

v. Central Limit Theorem (CLT)

ANSWERS: ** Answer box will enlarge as you type

B. What are the factors responsible to determine which test, parametric or non-parametric, is to be used in quantitative research? Explain with treatments and examples.

Answer 1

Following terms belong to the process where sample data is measured and used to make a statement about the population from which the sample is taken.

1)Significance level denotes the probability of rejection of a claim about the population when the claim is actually true. In more technical words that claim is nothing but our null hypothesis.if the value observed in the sample falls in the critical region, we reject the claim or the null hypothesis. it is the probability that sample results fall in the critical region.

2)When we select a sample of size n from a population of size N , a total of  N​C​​​​​n different samples can be selected. Statistic values obtained for these samples may be different for each samples. Which gives rise to sampling distribution. Thus distribution of a sample statistic is for all the samples is called a sampling distribution.

3)When a sample statistic is used a to give a finite estimate of population parameter , it is called a point estimator. For example sample mean is a point estimator of population mean.

4 )For a given statistic (by statistic we refer to a function of sample observation) it's standard deviation is called standard error and for a given significance level (alpha), margin of error is defined as Z​​​​​​alpha​ * standard error. Margin of error is nothing but allowable deviation for the given level of significance. Where Z is standard normal variate and Z(alpha) is nothing but critical values of Z at alpha level of significance.

5)According to Central limit theorem if X1,X2,...Xn are independent random variables with mean m1,m2,..and std deviation s1,s2,. ..respectively then

S= (X1+X2+X3+...Xn ) Will tend to follow normal distribution for large n. Or S will asymptotically follow normal distribution. With mean of S as sum of individual means and variance as sum of individual variances.

B)

Both parametric and non parametric methods are used in quantitative research but the main difference in the area of their uses is based on whether the form of population distribution is known or not.

When the form is known, then population parameters are estimated by parametric methods and when there is no assumption about the form of population, non parametric techniques is used for testing the hypothesis or the quantitative research.