6. With examples, provide a justification on why the third and fourth levels of
ID: 3374934 • Letter: 6
Question
6. With examples, provide a justification on why the third and fourth levels of hypotheses testing are more critical to a developmental agenda. [3 marks]. Noduve 7. Deductive and inductive reasoning are associated with the positivist philosophical orientation True or False? Provide a brief justification for your response. [4 marks] 8. Distinguish between the following types of variables and their implications for explaining associations and causal relations. [8 marks] a Moderating variable b. Instrumental variable-introduc c Confounding variable d. Endogenous variable and multipleExplanation / Answer
6 .Solution:
There are five steps involved a hypothesis testing which are given below:
1. Stating the Null and Alternative hypothesis.
2. Determine the appropriate Test-statistic.
3. Specify the level of significance.
4. Decision Rule.
5. Conclusion.
Here the third and fourth steps are the most crucial to a development agenda. We will discuss the importance of these two steps in detail given below,
Specifying the level of significance: In hypothesis testing a reseacher's main motive is to Reject the False null hypothesis or Do not reject the True null hypothesis. However there are possiblity of failing to reject the null hypothesis when it is false or rejecting the null hypothesis when it is true.
Rejecting the Null hypothesis when it is True is called the Type I error or Level of significance and it is denoted by lpha And failing to reject the null hypothesis when it is false is known as Type II error and it is denoted by eta.The best way to reduce both the errors is to increase the sample size, n.
Before data is collected researcher must specify the level of significance. The greater to desire is to not to reject a True null hypothesis, The lower the value of lpha we select. The level of significance can be between 0 and 1. Practically we used 0.1, 0.05 and 0.01 level of significance. Which results in 90%, 95% and 99% of not making a type I error respectively.
One should always choose a lower level of significance to get a statistically appropriate result.
Decision Rule: In this step we decide under what circumstances we should reject the null hypothesis or not at given level of significance. Here we find the critical value of the test-statistic, then we do not reject the null hypthesis if,
If our hypothesis is Left tailed, the Calculated value of the test statistics should be GREATER than Crtitical value of the test statistics.
If our hypothesis is Right tailed, the Calculated value of the test statistics should be LESS than Crtitical value of the test statistics.
If our hypothesis is Two tailed, the Calculated value of the test statistics should be BETWEEN the Crtitical values of the test statistics.
Hence, we can see how important these two steps are in a hypothesis testing. Let just take an example to understand it.
Example: A report claims that the Average life of a female is 57 years with a standard deviation of 4 years. To check this claim a statistician take a random sample of 50 females, she finds that the sample average life of the females is 62 years. Set a hypothesis to find that the claim is that population average life of females is 57 is statistically significant or population average life of females is different from 57 years, at 0.05 level of significance.
Solution: Given,
Population mean,mu = 57
Population standard deviation,sigma = 4
Sample size, n = 50
Sample mean,ar{x} = 62
1) Stating the hypothesis:
Let the null and alternative hypothesis be:
H0 : mu = 57
H1 : mu eq 57 (Two tailed)
2). Test-statistics:
Here n > 30, and population standard deviation is given, So, we will use Z-statistic here.
z = rac{ar{x}-mu}{ rac{sigma}{sqrt{n}}}
z = rac{62-57}{ rac{4}{sqrt{50}}}
z = 8.84
3). Level of significance: As given in the question level of significance, lpha = 0.05.
4). Decision Rule: The critical value of z = pm1.96 (lpha = 0.05) ( Two tailed hypothesis)
Here we will not reject the null hypothesis if, Calculated value of z-stats is between Critical value of z-stats.
5). Conclusion: Here, 8.84 > 1.96. The calculated value of z-stats is not between the Critical values( -1.96 , +1.96).
Hence we reject the Null hypothesis. So, at 0.05 level of significance with the given sample information we conclude that there are sufficient evidence to conclude that "Population average life of femals is different from 57."
7 SOLUTION:
This is False Statement:
Positivist philosophy is based on the real human experiences. It is more quantifiable, thus deductive reasoning are associated with the positivist orientation.
While inductive reasoning is related to the phenomenology philosophy.
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