A random sample is to be selected from a population that has a proportion of suc

Question

A random sample is to be selected from a population that has a proportion of successes = .7 a. Find the mean and the standard deviation of the sample proportion with a sample size of 9 b. What is the smallest value of n for which it is reasonable to assume that the sampling distribution of p is approx. normal? c. For a sample of n = 25 determine the approx. probability that the sample proportion will be within .25 of A random sample is to be selected from a population that has a proportion of successes = .7 a. Find the mean and the standard deviation of the sample proportion with a sample size of 9 b. What is the smallest value of n for which it is reasonable to assume that the sampling distribution of p is approx. normal? c. For a sample of n = 25 determine the approx. probability that the sample proportion will be within .25 of a. Find the mean and the standard deviation of the sample proportion with a sample size of 9 b. What is the smallest value of n for which it is reasonable to assume that the sampling distribution of p is approx. normal? c. For a sample of n = 25 determine the approx. probability that the sample proportion will be within .25 of

Explanation / Answer

here =0.7

a)hence mean =n =9*0.7 =6.3

and std deviation =(n(1-))1/2 =1.375

b) for normal approximation of binomial

n>5 and n(1-)>5

from above n>5/0.7 and n>5/0.3

from above n=17

c) for above std error =((1-)/n)1/2

                                 =0.0917

hence P((-0.25)<p<(+0.25)) =P(0.25/0.0917)<Z<0.25/0.0917)) =P(-2.728<Z<2.728) =0.9968- 0.0032 =0.9936

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