Appendix B.4 is a table of random numbers that are uniformly distributed. Hence,

Question

Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from 0 through (including) 9 has the same likelihood of occurrence. (Round your answers to 2 decimal places.)

Compute the population mean and standard deviation of the uniform distribution of random numbers.

Assume that 10 random samples of five values are selected from a table of random numbers. The results follow. Each row represents a random sample.

Compute the mean of each sample.

Compute the mean and standard deviation of the sample means. Compare the values to the population mean and standard deviation.

Sample 1 8 3 8 3 9 Sample 2 8 4 6 8 2 Sample 3 0 5 1 3 5 Sample 4 0 6 3 3 8 Sample 5 7 4 5 5 5

Explanation / Answer

Appendix B.4 is a table of random numbers that are uniformly distributed. Hence, each digit from 0 through (including) 9 has the same likelihood of occurrence.

Compute the population mean and standard deviation of the uniform distribution of random numbers.

We are given that the random numbers are uniformly distributed.

We know that for Uniform distribution the mean and variances are,

Population Mean = (a+b) / 2

Population Variance = (b - a)^2 / 12

Here a = 0 and b = 9

Population Mean = (a+b) / 2 = (0+9)/2 = 4.5

Population variance = (b - a)^2 / 12 = (9-0)^2/12 = 6.75

Assume that 10 random samples of five values are selected from a table of random numbers. The results follow. Each row represents a random sample.

Now we have to find mean and standard deviation for the five samples.

We can find this by using EXCEL.

syntax :

ENTER data into EXCEL sheet --> Data --> Data Analysis --> Descriptive statistics --> ok --> Input range : select all the data range --> Grouped by : columns --> Click on labels in first row --> Output Range : Select one empty cell --> Summary statistics --> ok

Compute the mean and standard deviation of the sample means.

Mean of sample mean = (6.2+5.6+2.8+4+5.2)/5 = 4.76

Standard deviation of sample mean = 6.75/sqrt(5) = 3.02

Population mean < sample of sample means

Population standard deviation > sample of sample standard deviation

sample1 sample2 sample3 sample4 sample5 mean 6.2 5.6 2.8 4 5.2 standard deviation 2.95 2.61 2.28 3.08 1.1

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