Question

"What are the correct notations for both the population parameter and the sample statistic for the following: mean and proportion? What distribution is appropriate for use with each parameter (assume the populations are normally distributed and the sample is small for the mean)? What is the formula for the test statistic when testing these parameters?"

Answer 1

a) Parameters :-

The statistical constants of the population namely mean 'μ' and variance σ²

are referred to as parameters.

b Statistics:-

The statistical computed from sample observations mean (x⁻) and variance

(S² ) are usually referred as statistics

c) the test statistic

`z= (x-mean)/((S.D)/(√(n) ) )`

Explanation:

Explanation:-

Population:-

Population consists of the totality of the observations with which we are concerned. This number is finite or infinite.

The number of observations in the population is defined to be the size of the population.

Sample:-

A sample is a subset of a population

Parameters :-

The statistical constants of the population namely mean 'μ' and variance σ²

are referred to as parameters.

Statistics:-

The statistical computed from sample observations mean (x⁻) and variance

(S² ) are usually referred as statistics

Central limit theorem:

If x⁻ is the mean of a random sample of size n taken from a population with mean 'μ' and finite variance σ² , then the limiting form of the distribution

`z= (x-mean)/((S.D)/(√(n) ) )`

Z- distribution:-

Suppose we want to test whether the given sample of size n has been drawn from a population with mean ''μ'

we set up null hypothesis that there is no significance between sample mean x⁻ and mean 'μ ' then The test statistic

`z= (x-mean)/((S.D)/(√(n) ) )`

standard deviation of the population parameter σ and sample statistic mean x⁻

Z- distribution for the given single proportion

Suppose we want to test whether the given sample of size n has been drawn from a normal population.

we set up null hypothesis that there is no significance between sample proportion 'p' and Population proportion 'P' then The test statistic

`z = \frac{p-P}{\sqrt{(PQ)/(n) } }`

Q =1-P