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Selecting a random sample is an example of a statistical experiment, and the sample statistic x is a numerical description of the result of the experiment. Therefore, x is a random variable. The probability distribution of x is called the sampling distribution of x. In practice, you select one random sample and use the information from that sample to estimate the population parameter of interest. However, statisticians sometimes perform a procedure called repeated sampling, in which the experiment is run over and over again and the value of the sample statistic from each running of the experiment is recorded. The distribution of the sample statistics from the repeated sampling is an.



Answer :

The smallest sample mean out of 1000 sample means is 133.273 ( minimum in table ) & largest sample mean is 166.887 (minimum in table ).

What does the word "sample" mean?

  • The arithmetic average of the values of a variable in a sample is used to get the sample mean, which is a statistic.
  • If the sample is chosen from probability distributions with a common anticipated value, then the sample mean is an estimate of that expected value.

X ≈ U ( 100 , 200 )                a = 100 , b = 200

E(X)  = a + b/2 = 150

Var(X) = (b - a )²/12 = 100²/2

sal(x) = √100²/2 = 50/√3  = 28.8675

E(X) = 150

Sd (x) ≈  sd(x)/√n  = 50/√3 . 1/√30 = 5.27046

The mean of the population is 150 [ E(x) ] , the mean of ( exact ) sampling distribution of x is also 150  [ E(x) ] , and the mean of the approximation of the sampling distribution of x is 150.123 .

The smallest sample mean out of 1000 sample means is 133.273 ( minimum in table ) & largest sample mean is 166.887 (minimum in table ).

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