A survey of 2,250 adults reported that 51% watch news videos. Complete parts (a) through (c) below. a. Suppose that you take a sample of 100 adults. If the population proportion of adults who watch news videos is 0.51, 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 0.51, 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 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 0.51 and decreases the probability in part (b). B. 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 0.51 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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 42PFA

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Question

A survey of 2,250 adults reported that 51%
watch news videos. Complete parts (a) through (c) below.

a.	Suppose that you take a sample of 100 adults. If the population proportion of adults who watch news videos is 0.51, 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 0.51, 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.

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 0.51 and decreases the probability in part (b).

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 0.51
and increases the probability in part (b).

The probabilities in parts (a) and (b) are the same. Increasing the sample size does not change the sampling distribution of the proportion.

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