SE 50B XP My Notes Ask Your Teacher What do you think is the ideal number of chi

Question

SE 50B XP My Notes Ask Your Teacher What do you think is the ideal number of children for a family to have?" A Gallup Poll asked this question of 1016 randomily chosen adults. Almost half (49%) thought two children was ideal, t 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 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 . 350? (Round your answer to four decimal places.) what is the probability that a sample proportion jp fails between 0.46 and 0.52 if the sample is an SRS of size n- 5000? (Round your answer to four decimal places.) Combine these results to make a general statement about the effect of larger samples in a sample survey O Larger samples give a smaller probability that p will be close to the true proportion p. Larger samples have no effect on the probability that p will be dose to the true proportion p. OLarger samples give a larger probabity that p will be close to the true proportion p. -n points MirtroSa 5E510.XP My Notes Ask Your Tead

Explanation / Answer

Given, p = 0.49 and n = 350
Standard error of the proportion = sqrt(p(1-p)/n) = sqrt(0.49(1-0.49)/350) = 0.0267

Z value for p = 0.46 is (0.46 - 0.49)/ 0.0267 = -1.12
Z value for p = 0.52 is (0.52 - 0.49)/ 0.0267 = 1.12
P(0.46 < p < 0.52) = P(-1.12 < Z < 1.12) = P(Z < 1.12) - P(Z < -1.12)
= 0.8686 - 0.1314 = 0.7372

Now, n = 5000
Standard error of the proportion = sqrt(p(1-p)/n) = sqrt(0.49(1-0.49)/5000) = 0.007

Z value for p = 0.46 is (0.46 - 0.49)/ 0.007 = -4.28
Z value for p = 0.52 is (0.52 - 0.49)/ 0.007 = 4.28
P(0.46 < p < 0.52) = P(-4.28 < Z < 4.28) = P(Z < 4.28) - P(Z < -4.28)
= 0.9999 - 0 = 0.9999 (or 1)

So, the correct option is,
Large samples give larger probability that p^ will be close to the true proportion p

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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