Question

In: Statistics and Probability

A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions...

A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 506 randomly selected Texans surveyed, 436 were in favor of the initiative and of the 525 randomly selected New Yorkers surveyed, 459 were in favor of the initiative.

a. With 90% confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between _______ (round to 3 decimal places) and ________ (round to 3 decimal places).

b. If many groups of 506 randomly selected Texans and 525 randomly selected New Yorkers were surveyed, then a different confidence interval would be produced from each group. About ___________ percent of these confidence intervals will contain the true population proportion of the difference in the proportions of Texans and New Yorkers who favor a new Green initiative and about _________________ percent will not contain the true population difference in proportions.

Solutions

Expert Solution

Solution:

Given that n = 506, x = 436

a. Then the 90% confidence interval for the true proportion (p) is
p̂ ± Zα/2 * sqrt(p̂(1-p̂)/n) where,
p̂ = x/n = 436/506 = 0.8617
q-hat = 1- p̂ = 1- 0.8617 = 0.1383 and
Level of significance α = 1-0.90 = 0.10
Zα/2 = Z0.05 = 1.645
Confidence interval CI = p̂ ± Zα/2 * sqrt(p̂(1-p̂)/n)
= 0.8617 ± 1.645 *sqrt(0.8617 (1-0.8617 )/506)
= 0.8617 ± 0.0252
= [0.837, 0.887]
With 90% confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between 0.837 and 0.887

b. If many groups of 506 randomly selected Texans and 525 randomly selected New Yorkers were surveyed, then a different confidence interval would be produced from each group. About 90 percent of these confidence intervals will contain the true population proportion of the difference in the proportions of Texans and New Yorkers who favor a new Green initiative and about 10% percent will not contain the true population difference in proportions.


Related Solutions

A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions...
A newsgroup is interested in constructing a 90% confidence interval for the difference in the proportions of Texans and New Yorkers who favor a new Green initiative. Of the 582 randomly selected Texans surveyed, 428 were in favor of the initiative and of the 569 randomly selected New Yorkers surveyed, 456 were in favor of the initiative. . With 90% confidence the difference in the proportions of Texans and New Yorkers who favor a new Green initiative is between (round...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 593 randomly selected Americans surveyed, 350 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between ? and ? . b. If many groups of 593 randomly selected Americans were surveyed, then...
1. A newsgroup is interested in constructing a 90% confidence interval for the proportion of all...
1. A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 526 randomly selected Americans surveyed, 353 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between____ and ____ . b. If many groups of 526 randomly selected Americans were surveyed, then...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 588 randomly selected Americans surveyed, 354 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 90% confidence the proportion of all Americans who favor the new Green initiative is between ___?__ and __?___ b. If many groups of 588 randomly selected Americans were surveyed, then a...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all americans...
A newsgroup is interested in constructing a 90% confidence interval for the proportion of all americans who are in favor of a new green initiative. Of the 560 randomly selected Americans surveyed, 392 were in favor of the initiative. a. With 90% confidence the proportion of all Americans who favor the new green initiative is between ___ and ___.
A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 590 randomly selected Americans surveyed, 410 were in favor of the initiative. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 590 randomly selected Americans were surveyed, then a different...
A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 534 randomly selected Americans surveyed, 400 were in favor of the initiative. a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between -- and --. b. If many groups of 534 randomly selected Americans were surveyed, then a different confidence interval would be produced from each...
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 99% confidence interval for the proportion of all Americans...
A newsgroup is interested in constructing a 99% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 596 randomly selected Americans surveyed, 394 were in favor of the initiative. a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between and . b. If many groups of 596 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...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT