A Pew Poll conducted in 2017 surveyed a random sample of 200 adult Americans and 75...

A Pew Poll conducted in 2017 surveyed a random sample of 200 adult Americans and 75 of them said that they had seen a ghost. Find a 99% confidence interval for the percentage of all Americans who believe they have seen a ghost. Interpret your interval. Round to three decimal places.

Solutions

Expert Solution

Solution :

Given that,

n = 200

x = 75

Point estimate = sample proportion = = x / n = 75/200=0.375

1 - = 1- 0.375 =0.625

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

Margin of error = E = Z / 2 * ( $\sqrt$ ((( * (1 - )) / n)

= 2.576* ( $\sqrt$ ((0.375*0.625) /200 )

E = 0.088

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.375-0.088< p <0.375+ 0.088

0.287< p < 0.463

The 99% confidence interval for the population proportion p is0.287, 0.463

orchestra answered 1 year ago

Next > < Previous

Related Solutions

In March 2014, Harris Interactive conducted a poll of a random sample of 2234 adult Americans...

In March 2014, Harris Interactive conducted a poll of a random sample of 2234 adult Americans 18 years of age or older and asked, "which is more annoying to you, tailgaters or slow drivers who stay in the passing lane?" Among those surveyed, 1184 were more annoyed by tailgaters a) Explain why the variable of interest is qualitative with two possible outcomes. What are the two outcomes? b) Verify the requirements for constructing a 90% confidence intervsl for the population...

A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots...

A Pew Research study conducted in 2017 found that approximately 75% of Americans believe that robots and computers might one day do many of the jobs currently done by people.† Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated. Nurse Tax Auditor Fast-Food Worker 4 4 6 5 5 7 5 4 6 2 3 8...

A poll conducted in 2013 surveyed a random sample of 2003 American adults, and 18% of...

A poll conducted in 2013 surveyed a random sample of 2003 American adults, and 18% of them said that they have seen a ghost. Construct a 95% confidence interval for the proportion of American adults who have seen a ghost.

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic...

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, test the claim that at least half of all voters prefer the Democrat. State the sample percentage and sample size.

A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic...

Data from a random sample of 2300 adult Americans found that 1300 of those surveyed would...

Data from a random sample of 2300 adult Americans found that 1300 of those surveyed would prefer to live in a hot climate rather than a cold climate. Do the sample data provide convincing evidence that a majority of all adult Americans prefer a hot climate over a cold climate? (a) State the null and alternative hypotheses to be tested. (b) Test the relevant hypotheses using α = .01. (Be sure to check all necessary conditions and clearly state your...

Video games In a poll of 1,063 randomly selected adult gamers conducted by the Pew Internet...

Video games In a poll of 1,063 randomly selected adult gamers conducted by the Pew Internet Project, 54% of the adult gamers interviewed reported that they used a gaming console (such as an Xbox 360, PS3 or Wii) to play video games. In a separate Pew study, 89% of 1,064 randomly selected teen gamers reported that they used a gaming console. Perform a hypothesis test to evaluate the claim that teen gamers are more likely to use a gaming console...

A poll of 1000 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency.

A poll of 1000 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, do the data provide sufficient evidence to conclude that the percentage of voters who prefer the Democrat is less than 50%?

5. In a random sample of 200 adult Americans, 8 had some form of color blindness....

5. In a random sample of 200 adult Americans, 8 had some form of color blindness. a. Construct and interpret a 95% confidence interval using the Wilson-adjusted method. b. Using the information above as a pilot study, how many adult Americans would need to be sampled in order to estimate the population proportion with a standard error of no more than 0.005? c. If no prior estimate of the prevalence of color blindness was available, how many adult Americans would...

15. As part of the Pew Internet and American Life Project, researchers surveyed a random sample...

15. As part of the Pew Internet and American Life Project, researchers surveyed a random sample of 800 teens and a separate random sample of 400 young adults. For the teens, 79% said that they own an iPod or MP3 player. For the young adults, this figure was 67%. Is there a significant difference between the population proportions? State appropriate hypotheses for a significance test to answer this question. Define any parameters you use. 17. Refer to Exercise 15. a)....

Subjects