Question

Describe an example of a study that will come under each of the following categories

A test of difference for

One sample

            Means

            Proportion

Two independent samples

            Means

            Proportion

Paired sample

            Means

            Proportion

More than two sample

            Means

            Proportion

Answer 1

1) One sample

a) Mean: A soft-drink company claims that it fills its bottles with certain amout of drink. However, a customer suspects that the amount is less than what the company claims.

b) Proportion: An insurance company sells 3 different types of insurance plans. A researcher is interested in knowing the proportion of one of the types of insurances sold.

2) Two independent samples

a) Mean: Two groups of people undergo two different types of training programs. The researcher is interested in knowing whether mean efficiency of the people given the two different programs are equal or not.

b) Proportion: Elections have just happened. It is of interest whether the proportions of males and females who have cast their votes are equal or not.

3) Paired sample

a) Mean: We want to check the effectiveness of a certain diet in increasing the weight of children. The weights of a sample of children are noted, they are given the diet for some duration, say 1 week or so and then the weights of the children are measured again. The difference in the two weights would help in determining the effectiveness of the diet.  

b) Proportion: The effectiveness of a new vaccine is to be tested. It is of interest whether the vaccine has decreased the chances of a person developing symptoms of the disease.

4) More than two samples:

a) Mean: There are three different fertilizers and a person is interested in knowing which fertilizer results in the best growth oh the plants. So, the three fertilizers would be administered to say n1, n2 and n3 plants respectively and the sample means for the three categories would be tested for equality of the population means.

b) Proportion: Elections have just happened. It is of interest whether the proportions of males, females and LGBTQ+ who have cast their votes are equal or not.

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