Question

1.A study was done to determine whether there is a relationship between snoring and the risk of heart disease. Among 1,105 snorers in the study, 86 had heart disease, while only 29 of 1,379 nonsnorers had heart disease.

(a)Determine a 95% confidence interval that estimates p₁ − p₂ = difference in proportions of snorers and nonsnorers who have heart disease. (Let p₁ be the proportion of snorers and p₂be the proportion of nonsnorers. Round your answers to three decimal places.)

2.In a certain survey, a question asked is whether a respondent favors or opposes capital punishment (the death penalty) for persons convicted of murder. The output for this exercise compares the proportions who said that they were opposed to the death penalty in the year 2000 and the year 1993.

Sample	X	N	Sample p
2000	701	2685	0.261
1993	337	1488	0.226

Estimate for p(1) - p(2): 0.035

(a) Find the value of s.e.(p̂₁ - p̂₂) = standard error of the difference between the two sample proportions. (Round the answer to four decimal places.)
s.e.(p̂₁ - p̂₂) =
Also, find a 90% confidence interval for the difference between the population proportions opposed to the death penalty in the years 2000 and 1993. (Round the answers to three decimal places.)

3. In a survey, 95% of n = 348 randomly sampled married men said that they would marry their spouses again if they had it to do all over again. In the same survey, 85% of n = 525 married women said that they would marry their spouses if they had it to do all over again.

Calculate a 95% confidence interval that estimates the difference in proportions of married women and men who would marry their spouse again if they had it to do all over again.(Round your answers to three decimal places.)

Answer 1

the first part of the solution showing derivation of the confidence interval for p1-p2.

the second part of the derivation.

the final part of the derivation showing the form of the confidence interval for p1-p2.

the computation of the confidence interval for 1(a).

the first part of the solution for 2(a).

the final part of the solution for 2(a).

the first part of the solution for (3).

thes final part of the solution for (3).