Question

1. Explain, what type of data would it be most appropriate to use a mean and what type of data would it be most appropriate to use a proportion?
2. We typically use the t distribution when working with means, and yet we always use the normal (z) distribution when working with proportions. Try to explain in your own words why this is the case.
3. Write TWO situations: (a) one that can be answered using a z-interval for a proportion, (b) one that can be answered using a t-interval for a mean.

Answer 1

In above question, there are two distribution

1) t distribution

2) normal(z) distribution

The use of this two distribution depends on the sample size we have to taken in our example.

1) t distribution - It is used in Small sample test ( Sample size less than 30), when we use the t-distribution for means then the sample size is must be less than 30

and if sample size is less than 30 (sample size n < 30) for one sample data or two sample data

(sample size n1, n2 < 30) and Population variance is not known then in such a case it is better to use of t-distribution than normal(z) distribution.

2) normal(z) distribution - It is used in Large sample test ( Sample size greater than 30), when we use normal distribution the sample size is greater than 30 for all types sample data set (sample size n >30). When we have to find proportions then we use normal(z) distribution.

Formulae of finding t-distribution and normal distribution are approximately same but it's use depend on sample size we have to taken.