Question

In: Statistics and Probability

A pollster wants to construct a 95% confidence interval for the proportion of all U.S. adults...

  1. A pollster wants to construct a 95% confidence interval for the proportion of all U.S. adults who believe that economic conditions are getting better under President Donald Trump. How large a sample should the pollster take so that the estimate is within 3.0% of the true population proportion? [4]

Solutions

Expert Solution

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 3% = 0.03

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.96 / 0.03)2 * 0.5 * 0.5

= 1067.11

Sample size =1067


Related Solutions

How's the economy? A pollster wants to construct a 99.5% confidence interval for the proportion of...
How's the economy? A pollster wants to construct a 99.5% confidence interval for the proportion of adults who believe that economic conditions are getting better. (a) A poll taken in July 2010 estimates this proportion to be 0.3 Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02? A sample of adults is needed to obtain a 99.5% confidence interval with a margin of error of 0.02 . B....
27. Call me: A sociologist wants to construct a 95% confidence interval for the proportion of...
27. Call me: A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–10 living in New York who own a cell phone. a. A survey by the National Consumers League estimated the nationwide proportion to be 0.32. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02? b. Estimate the sample size needed if no estimate of p is available. c. If the...
Construct a 95​% confidence interval to estimate the population proportion with a sample proportion equal to...
Construct a 95​% confidence interval to estimate the population proportion with a sample proportion equal to 0.45 and a sample size equal to 120. ----- A 95% confidence interval estimates that the population proportion is between a lower limit of ___ and an upper limit of ___ ????
Use the formulas provided in class to construct a 95% confidence interval for the proportion of...
Use the formulas provided in class to construct a 95% confidence interval for the proportion of all Americans who have blue eyes. - Interpret this confidence interval in the context of the research question. - It is claimed that blue eyes are becoming less common, and it estimated that in 2006, one out of six Americans had blue eyes. Do a hypothesis test to see if our class provides evidence that blue eyes are becoming less common. What are the...
7. A 95% confidence interval for the proportion of adults in Portland who have an iPhone...
7. A 95% confidence interval for the proportion of adults in Portland who have an iPhone is (0.303, 0.437). Find the number of people in the sample.7. A 95% confidence interval for the proportion of adults in BBC who have an iPhone is (0.303, 0.437). Find the number of people in the sample??
Construct a 95% confidence interval by hand for what proportion of students are vegan, if you...
Construct a 95% confidence interval by hand for what proportion of students are vegan, if you took a random sample of 100 students and 3 were vegan.
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 537 randomly selected Americans surveyed, 368 were in favor of the initiative. a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 537 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group....
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 555 randomly selected Americans surveyed, 385 were in favor of the initiative. Round answers to 2 decimal places where possible. a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 555 randomly selected Americans were surveyed, then a different...
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 539 randomly selected Americans surveyed, 442 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all Americans who favor the new Green initiative is between ____and _____ . b. If many groups of 539 randomly selected Americans were surveyed, then a...
Construct a? 95% confidence interval to estimate the population proportion using the data below. x =...
Construct a? 95% confidence interval to estimate the population proportion using the data below. x = 29 n = 90 N = 500 The? 95% confidence interval for the population proportion is? (_,_).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT