Question

Q.1. A population consists of five numbers 2, 4, 5, 8, 12. (i) List all possible samples of size 2 that can be drawn from this population with replacement. (ii) Construct the sampling distribution of the samples mean drawn in part (i). (iii) Verify that mean of the sampling distribution is equal to the population mean and δ = δ/ .

solve the above problem step by step in proper format

Answer 1

I have Minitab software for above problem.

Steps1)In the 1st column enter the population Values 2,4,5,8,12.

Step2) Select-> Random Data -> Select Sample From Columns -> Double Click.

Step3) Enter in Number of rows to sample: 1000

select -> Stat-> Basic Statistics ->Store Descriptive statistics.

Stat-> Basic Statistics-. Graphical Summary->In variable enter sample mean and confidence interval interval=95.0 -> ok.

Then the above graph shows mean of sampling distribution of population. From graph sample mean=6.2045 and sample standard deviation= sigma/√n = 2.4336

And for population,

From descriptive statistics: Population

Mean = 6.20

And standard deviation= 3.90

Mean and standard deviation of sampling mean from the population is approximately equal to population mean and population standard deviation.