A survey of 2150 adults reported that 56% watch news videos. Complete parts (a)

Question

A survey of 2150 adults reported that 56% watch news videos. Complete parts (a) through (c) below. a. Suppose that you take a sample of 50 adults. If the population proportion of adults who watch news videos is 0.56, what is the probability that fewer than half in your sample will watch news videos? The probability is nothing that 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 250 adults. If the population proportion of adults who watch news videos is 0.56, what is the probability that fewer than half in your sample will watch news videos? The probability is nothing that fewer than half of the adults in the sample will watch news videos. (Round to four decimal places as needed.) c. Discuss the effect of sample size on the sampling distribution of the proportion in general and the effect on the probabilities in parts (a) and (b). Choose the correct answer below. A. The probabilities in parts (a) and (b) are the same. Increasing the sample size does not change the sampling distribution of the proportion. B. Increasing the sample size by a factor of 5 decreases the standard error by a factor of StartRoot 5 EndRoot. This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.56 and decreases the probability in part (b). C. Increasing the sample size by a factor of 5 increases the standard error by a factor of StartRoot 5 EndRoot. This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.56 and increases the probability in part (b).

Explanation / Answer

a)

  probability that fewer than half in your sample will watch news videos:

b)

  B. Increasing the sample size by a factor of 5 decreases the standard error by a factor of SquaretRoot 5 EndRoot. This causes the sampling distribution of the proportion to become more concentrated around the true population proportion of 0.56 and decreases the probability in part

for normal distribution z score =(p-p)/p here population proportion=     p= 0.560 sample size       =n= 50 std error of proportion=p=(p*(1-p)/n)= 0.070

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