Question

A random sample is to be selected from a population that has a proportion of successes p = 0.61. Determine the mean and standard deviation of the sampling distribution of p̂ for each of the sample sizes (round to 3 decimal places).

a. n = 9

Mean:

Standard deviation:

b. n = 19

Mean:

Standard deviation:

c. n = 28

Mean:

Standard deviation:

d. n = 43

Mean:

Standard deviation:

e. n = 102

Mean:

Standard deviation:

Answer 1

Solution :-

Given :- p = 0.61 ,

a)

For ,n = 9

Mean ( p ) = = 0.61

standard deviation ( ) is,

= p ( 1 - p ) / n

= 0.61 ( 1 - 0.61 ) / 9

= 0.163

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b)

For ,n = 19

Mean ( p ) = = 0.61

standard deviation ( ) is,

= p ( 1 - p ) / n

= 0.61 ( 1 - 0.61 ) / 19

= 0.112

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c)

For ,n = 28

Mean ( p ) = = 0.61

standard deviation ( ​​​​​​​ ) is,

= p ( 1 - p ) / n

= 0.61 ( 1 - 0.61 ) / 28

= 0.092

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d)

For ,n = 43

Mean ( p ) = = 0.61

standard deviation ( ​​​​​​​ ) is,

= p ( 1 - p ) / n

= 0.61 ( 1 - 0.61 ) / 43

= 0.074

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e )

For ,n = 102

Mean ( p ) = = 0.61

standard deviation ( ​​​​​​​ ) is,

= p ( 1 - p ) / n

= 0.61 ( 1 - 0.61 ) / 102

= 0.048