A survey of 2,350 adults reported that 55% watch news videos. Complete parts (a)

Question

A survey of 2,350 adults reported that 55% watch news videos. Complete parts (a) through (c) below. Suppose that you take a sample of 100 adults. If the population proportion of adults who watch news videos is 0.55, what is the probability that fewer than half in your sample will watch news videos? a. The probability isthat fewer than half of the adults in the sample will watch news videos (Round to four decimal places as needed.) b. Suppose that you take a sample of 500 adults. If the population proportion of adults who watch news videos is 0.55, what is the probability that fewer than half in your sample will watch news videos? The probabity is that fewer than half of the adults in the sampie will watch news videos (Round to four decimal places as needed.) C. Choose the correct answer beloW 0 A. The probabilities in parts (a) and (b) are the same. Increasing the sample size does not change the sampling distribution of the proportion O B Increasing the sample size by a factor of 5 decreases the standard error by a factor of 5 This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.55 and decreases the probability in part (b) OC. Increasing the sample size by a factor of 5 increases the standard error by a factor of 5. This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.55 and increases the probability in part (b)

Explanation / Answer

a) here std error =(P(1-p)/n)1/2 =0.0497

thereforeprobability=P(X<0.5)=P(Z<(0.5-0.55)/0.0497)=P(Z<-1.005)=0.1574

b)

std error =(P(1-p)/n)1/2 =0.0222

thereforeprobability=P(X<0.5)=P(Z<(0.5-0.55)/0.0222)=P(Z<-2.2473)=0.0123

c)

option B is correct

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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