Knowee
Questions
Features
Study Tools

A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.Due to a limited budget, the researcher obtained opinions from a random sample of only 1,432 U.S. adults. With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than which of the following percentages (answers are rounded)? 0.07% 2.6% 3.0% 5.2%

Question

A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.Due to a limited budget, the researcher obtained opinions from a random sample of only 1,432 U.S. adults. With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than which of the following percentages (answers are rounded)? 0.07% 2.6% 3.0% 5.2%

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

To answer this question, we need to use the formula for the margin of error for a proportion, which is given by:

E = Z * sqrt[(p(1-p))/n]

Where:

  • E is the margin of error
  • Z is the Z-score (which is 1.96 for a 95% confidence level)
  • p is the estimated proportion (we don't know this, so we'll use the most conservative estimate of 0.5)
  • n is the sample size

Substituting the values into the formula, we get:

E = 1.96 * sqrt[(0.5(1-0.5))/1432] E = 1.96 * sqrt[0.25/1432] E = 1.96 * sqrt[0.0001745] E = 1.96 * 0.0132 E = 0.0259

So, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than 2.6%.

This problem has been solved

Similar Questions

A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples. Due to a limited budget, the researcher obtained opinions from a random sample of only 2,222 U.S. adults.With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than which of the following percentages (answers are rounded)? 0.04% 0.75% 2.1% 3%Question 13Select one answer.10 pointsA researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.If the researcher would like to be 95% sure that the obtained sample proportion would be within 2.4% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 6,945 1,737 435 42

A researcher would like to estimate p, the proportion of U.S. adults who support raising the federal minimum wage.If the researcher would like to be 95% sure that the obtained sample proportion would be within 2.4% of p (the proportion in the entire population of U.S. adults), what sample size should be used? 6,945 1,737 435 42

A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people.Which of the following is true regarding the sample proportion p̂ of "yes" responses? The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p. The sample proportion from sample of 100 is more likely to be close to the true population proportion, p. The sample proportion in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase.How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)?(Hint: Use the sampling distribution of the sample proportion in this case.) It is certain that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 99.7% chance that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 68% chance that the resulting sample proportion will be within 0.04 of the true proportion.

A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.