Dear Expert,Can you solve for me this problem please. Use a random-number genera

Question

Dear Expert,Can you solve for me this problem please.

Use a random-number generator to obtain a sample of four digits between 0 and 9. You can do this using excel and the function =RANDBETWEEN(0, 9). a. Do so a total of 50 times and compute the mean of each sample. You can do this using the excel function =AVERAGE( )

b. Theoretically, what are the mean and standard deviation of all possible sample means for samples of size 4?

c. Roughly what would you expect the mean and standard deviation of the 50 sample means you obtained in part (a) to be? Explain why.

d. Determine the mean and standard deviation of the 50 sample means you obtained in part (a). You can do this using the excel functions =AVERAGE( ) and =STDEV( ).

e. Compare your answers in parts (c) and (d). Why are they different?

Explanation / Answer

Part-a

following are calculations

Part-b

Mean of 10 digitst = (0+1+...+9)/10=4.5 and standard deviation sigma=3.03

Theoretically, the mean and standard deviation of all possible sample means for samples of size 4 should me mu =4.5 and sigma/sqrt(4) =3.03/2=1.515 where Mu and Sigma are population and standard deviations

c. Roughly we expect the mean and standard deviation of the 50 sample means you obtained in part (a) to be mu=4.5 and sigma/sqrt(50)=3.03/sqrt(50)=0.43

d. The mean and standard deviation of the 50 sample means are 4.85 and 0.88

e. These are different due to sampling fluctutations

Sample s1 s2 s3 s4 s5 s6 s7 s8 s9 s10 s11 s12 s13 s14 s15 s16 s17 s18 s19 s20 s21 s22 s23 s24 s25 s26 s27 s28 s29 s30 s31 s32 s33 s34 s35 s36 s37 s38 s39 s40 s41 s42 s43 s44 s45 s46 s47 s48 s49 s50 1 0 4 9 2 3 6 4 0 9 2 8 5 1 7 5 0 2 7 5 8 7 5 3 6 7 7 9 8 6 3 5 4 9 2 7 9 0 9 8 5 4 7 2 4 4 3 4 5 4 6 2 9 5 5 5 7 8 7 4 2 9 6 9 9 4 3 8 6 2 9 7 6 5 5 7 0 7 8 0 7 6 0 6 3 2 0 6 1 2 7 0 1 7 0 2 6 9 1 0 7 2 3 6 5 9 6 2 4 6 9 3 5 8 7 0 1 8 6 3 0 2 1 3 0 5 3 3 9 5 9 2 0 5 2 4 9 2 6 6 0 7 0 9 3 4 6 7 6 9 8 6 5 4 8 6 4 5 6 5 8 3 7 1 0 1 9 2 7 8 8 5 6 1 2 8 8 0 6 3 7 1 5 5 0 9 9 1 5 8 7 9 1 2 4 9 9 3 1 7 3 4 5 8 Mean 6 5 7 5 5 6 6 4 5 4.3 5.5 5.5 4.8 3.5 5.8 5.5 4.8 3.5 5.5 4.3 4.5 4.5 5.3 4 4 6.5 7.3 4.5 5 3.5 2.5 5.3 6.3 3.5 3.5 7.3 3.5 5 5.8 1.8 4.5 6.5 3.8 3.8 4.5 6.3 4.3 4.3 5.5 5.3 4.85 Mean SD 4 1 3 2 2 2 2 4 3 3.6 3.8 3.4 4.9 2.6 2.2 3.8 2.8 3.1 2.9 3.8 2.4 3.3 2.1 3.2 3.2 2.5 1.7 4.7 2.2 2.6 2.9 3 3.2 3.7 3.1 1.5 3.5 4.7 3.2 2.4 3.3 2.5 3.9 1.7 2.6 2.5 3.4 3.3 1.3 2.5 0.88 SD

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