"What do you think is the ideal number of children for a family
to have?" A Gallup Poll asked this question of 1016 randomly chosen
adults. Almost half (49%) thought two children was ideal.† We are
supposing that the proportion of all adults who think that two
children is ideal is p = 0.49.
What is the probability that a sample proportion p̂ falls
between 0.46 and 0.52 (that is, within ±3 percentage points of the
true p) if the sample is an SRS of size n =
200?(Round your answer to four decimal places.)
What is the probability that a sample proportion p̂ falls
between 0.46 and 0.52 if the sample is an SRS of size n =
5000? (Round your answer to four decimal places.)
1)
for normal distribution z score =(p̂-p)/σ_{p} | |
here population proportion= p= | 0.490 |
sample size =n= | 200 |
std error of proportion=σ_{p}=√(p*(1-p)/n)= | 0.0353 |
probability = | P(0.46<X<0.52) | = | P(-0.85<Z<0.85)= | 0.8023-0.1977= | 0.6046 |
2)
sample size =n= | 5000 |
std error of proportion=σ_{p}=√(p*(1-p)/n)= | 0.0071 |
probability = | P(0.46<X<0.52) | = | P(-4.24<Z<4.24)= | 1-0= | 1.0000 |
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