Question

Assume you wish to compare two distinct groups of people (e.g., men vs women; old vs young; those with college degree versus those without, those who shop online vs those who do not, etc.) Describe a situation where you would use one of the tests presented in this chapter, tests of goodness of fit, independence & multiple proportions. Identify the populations of interest; describe the research question; form the null and alternative hypotheses and the level of significance; the sample size and sampling procedure; and the test statistic and associated degrees of freedom.

Please provide realistic example

Answer 1

• Degrees of Freedom. Definition: The Degrees of Freedom refers to the number of values involved in the calculations that have the freedom to vary.
• In other words, the degrees of freedom, in general, can be defined as the total number of observations minus the number of independent constraints imposed on the observations.
• A statistical hypothesis is an assumption about a population parameter.
• This assumption may or may not be true. For instance, the statement that a population mean is equal to 10.
• Example of a statistical hypothesis: A researcher might conduct a statistical experiment to test the validity of this hypothesis.
• Suppose we want to compare the yearly expenditure on clothing of men and women .so our hypothesis would be, is there any significant difference in men's yearly expenditure on clothing and women's yearly expenditure on clothing.
• to test the hypothesis we would collect sample data on men's and women's yearly expenditure on clothing.
• To test the hypothesis we make null and alternative hypothesis as follows:
• H₀: µ_M= µ_W i.e: there is no significant difference in men's and women's yearly expenditure on clothing.
• H₀: µ_M# µ_{W i.e; there is a significant difference in men's and women's yearly expenditure on clothing.}
• To test the hypothesis we shall use two independent samples t test
• The t test statistic is given as follows:
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