ider asmall population of to s units, labeled 2, tis ith respect Y- vahe s 3,1,

Question

ider asmall population of to s units, labeled 2, tis ith respect Y- vahe s 3,1, o,1 t s Consider asimple om sampling desien voith a sample size n a a Ga nte directly the variance var of the sample mean and variance Yarcmy zf the semele n median Cho From each Sample e the sample vorrances and the estimate voir ng) of the rarance the sample meem. Shors Hnet the sample vor cance Sz i s un braced for the finite popnutiam vertemee that the sense s and deviation is not unbiased for natim standard deviation nstruc tor each me -eende confidence interval Por the actual coverage probabile Yneonn. and desi

Explanation / Answer

the given population is as below withtheir respective values:

N Y

1 3

2 1

3 0

4 1

5 5

Now we have to select a sample of three data values using random sampling. in random sampling every data value has an equal chance of getting selected. it doesnot follow any particular procedure to select them.

so, let's take a number randomly '2' that every 2nd data value in the population to make the sample. you can use excelalso to select random data values.

ok so now if we choose every second value in the population we draw the following sample

N Y

2 1

4 1

1 3

a) Now we have to calculate sample variance. Some students ake the mistake of finding variance of N but we have to find out the varince of responses i.e. Y

firstof all we have tofind out the mean of the sample

mean= 1+1+3/3 = 5/3 =1.66

variance = to calculate the variance we subtract mean from the responses Y and square them. these are then added and divided by the sample size. variance defines how much the values of the sample variates from the mean. The pupose of squaring them is that we dont get any negative value which can affect the results.

variance= (1-1.66)2+(1-1.66)2+(3-1.66)2/3 ==0.89

now we have to find out the variance of the sample according to medin of the sample.

Y= 1,1,3

the median of the samples the values in the centre that is 1 in this case.

so the meadian of the sample = 1

variance= (1-1)2+(1-1)2+(3-1)2/3=2/3= 0.66

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