A survey of 2,450 adults reported that 57?% watch news videos. Complete parts? (a) through? (c) below.
a. Suppose that you take a sample of100 adults. If the population proportion of adults who watch news videos is 0.57?, what is the probability that fewer than half in your sample will watch news? videos?
The probability is ________________ 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 500 adults. If the population proportion of adults who watch news videos is 0.57?, what is the probability that fewer than half in your sample will watch news? videos?
The probability is _____________ 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. Increasing the sample size by the factor of 5 decreases the standard error by the factor of sqrt. root of5. This causes the sampling distrubtion of the proportion to become more concentrated around the population of 0.57 and decreases the probability in part (b).
B. Increasing the sample size by the factor of 5 increases the standard error by the factor of sqrt. root of 5. This causes the sampling distrubtion of the proportion to become more concentrated around the true population proportion of 0.57 and increases the probability in part (b).
C. The probabilities in parts (a) and (b) are the same. Increasing the sample size does not change the sampling distribution of the proportion.