At the downtown office of First National Bank there are 5 tellers. Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.How many different samples of 2 tellers are possible? List all possible samples of size 2 and compute the mean of each Compute the mean of the sample means and compare it to the population mean. State the Central Limit Theorem.

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Description: At the downtown office of First National Bank there are 5 tellers. Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.How many different samples of 2 tellers are possible? List all possible samples of size 2 and compute

Number of errors made by teller are 2, 3, 5, 3, and 5. 1) How many different samples of 2 tellers are possible? Total number of tellers in the population is N=5 sample size n=2 Total number of possible sample size of 2 is Formula: Ncn=N!/(N-n)!n! =5!/(5-2)!2! =120/12 =10 Let Xi be the ith sample of size 2. so, Xi-bar=(Xi1+Xi2)/2 Result: The Total number of possible sample size of 2 is 10 2) List all possible samples of size 2 and compute the mean of each sample means of all possible samples of size 2 is given in the below table sample values sum ∑j Xij Mean Xi-bar 1 2.3 5 2.5 2 2.5 7 3.5 3 2.3 5 2.5 4 2.5 7 3.5 5 3.5 8 4 6 3.3 6 3 7 3.5 8 4 8 5.3 8 4 9 5.5 10 5 10 3.5 8 4 3)Compute the mean of the sample means and compare it to the population mean. Population mean(μ)=2+3+5+3+5/5 =18/5 Population mean(μ)=3.6 sampling distribution of the sampling mean n=2 is as follows Sample means Number of means Probability 2.5 2 0.2 3 1 0.1 3.5 2 0.2 4 4 0.4 5 1 0.1 The sample mean μxbar=sum of all sample means/total no of samples =(2.5*2+3*1+3.5*2+4*4+5*1)/10 =5+3+7+16+5/10 =36/10 sample mean μxbar =3.6 this shows that μxbar=μ Result: μxbar(3.6)=μ(3.6) 4)State the Central Limit Theorem: The Central limit theorem states that, if we have a population with mean μ and standard deviation σ and take sufficiently large random sample from population with replacement, then the distribution of sample means will be approximately normally distributed.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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At the downtown office of First National Bank there are 5 tellers. Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.
1. How many different samples of 2 tellers are possible?
2. List all possible samples of size 2 and compute the mean of each
3. Compute the mean of the sample means and compare it to the population mean.
4. State the Central Limit Theorem.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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