Confidence interval for difference of proportions

A question is this type if and only if it asks to construct a confidence interval for p₁ - p₂ from two independent samples of proportions.

2 questions · Standard +0.3

5.05d Confidence intervals: using normal distribution
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AQA S3 2009 June Q1
8 marks Standard +0.3
1 An analysis of a random sample of 150 urban dwellings for sale showed that 102 are semi-detached. An analysis of an independent random sample of 80 rural dwellings for sale showed that 36 are semi-detached.
  1. Construct an approximate \(99 \%\) confidence interval for the difference between the proportion of urban dwellings for sale that are semi-detached and the proportion of rural dwellings for sale that are semi-detached.
  2. Hence comment on the claim that there is no difference between these two proportions.
AQA S3 2011 June Q5
8 marks Standard +0.3
5
An examination of 160 e-mails received by Gopal showed that 72 had attachments. An examination of 250 e-mails received by Haley showed that 102 had attachments.
Stating two necessary assumptions about the selection of e-mails, construct an approximate \(99 \%\) confidence interval for the difference between the proportion of e-mails received by Gopal that have attachments and the proportion of e-mails received by Haley that have attachments.
(8 marks)