High School

We appreciate your visit to A survey of 2 350 adults reported that 54 watch news videos Complete parts a through c below a Suppose that you take a sample. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A survey of 2,350 adults reported that 54% 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 0.54, what is the probability that fewer than half in your 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 0.54, what is the probability that fewer than half in your 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 0.54 and decreases the probability in part (a).

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

C. 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 0.54 and increases the probability in part (b).

Answer :

The effect of increasing the sample size concentrates the sampling distribution around the true population proportion and generally decreases the probability of a specific outcome. Thus, option A is correct.

The probability that less than half of the sample watches news videos drops when the sample size increases from 50 to 250 adults. In general, increasing sample size concentrates the sampling distribution around the true population proportion, decreasing the probability of a specific outcome.

This question pertains to probability and sampling distribution in statistics. If the population proportion (P) is 0.54, then the probability (Q) of not watching news videos is 1-P = 0.46. For a sample of size n=50, the standard error (SE) is sqrt[PQ/n] = sqrt[(0.54*0.46)/50] = 0.070. To find the probability that fewer than half (0.5) in your sample will watch news videos, we normalize and find z = (0.5-0.54)/SE = -0.57. Using a z-table, this probability is approximately 0.2843.

When we increase the sample size to n=250, the SE = sqrt[(0.54*0.46)/250] = 0.031. The z-score is (0.5-0.54)/SE = -1.29. The probability this time is around 0.0985. Hence, the probability decreases with a larger sample size.

By concentrating the sampling distribution around the true population percentage, increasing the sample size has the effect of lowering the likelihood of a particular event. Therefore, choice A is right.

Learn more about the topic of Sampling Distribution here:

https://brainly.com/question/31520808

#SPJ11

Thanks for taking the time to read A survey of 2 350 adults reported that 54 watch news videos Complete parts a through c below a Suppose that you take a sample. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada