\"What do you think is the ideal number of children for a family to have?\" A Ga

Question

"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 p 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 = 450? (Round your answer to four decimal places.)

What is the probability that a sample proportion p falls between 0.46 and 0.52 if the sample is an SRS of size n = 5000? (Round your answer to four decimal places.)

Explanation / Answer

a)

here for p=0.49 and n=450

std error =(p(1-p)/n)1/2 =0.0236

therefore  probability that a sample proportion p falls between 0.46 and 0.52 =P(0.46<p<0.52)

=P((0.46-0.49)/0.0236<Z<(0.52-0.46)/0.0236) =P(-1.2730<Z<1.2730)=0.8985-0.1015 =0.7970

b)

for p=0.49 and n=5000

std error =(p(1-p)/n)1/2 =0.0070

therefore  probability that a sample proportion p falls between 0.46 and 0.52 =P(0.46<p<0.52)

=P((0.46-0.49)/0.0071<Z<(0.52-0.46)/0.0071) =P(-4.2435<Z<4.2435)=~1.0000-~0.0000 =~ 1.0000

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.