A researcher wishes to estimate with 90 confidence the propo

A researcher wishes to estimate, with 90% confidence, the proportion of adults who have high-speed internet access. Her estimeate must be accurate within 3% of the true proportion.

a) Find the minimum samply size needed, using a prior study that found that 32% of the respondents said they have high-speed internet access.

b) No preliminary estimate is available. Find the minimum sample size needed.

Solution

Given a=0.1, Z(0.05) = 1.65 (from standard normal table)

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(a) n=(Z/E)^2*p*(1-p)

=(1.65/0.03)^2*0.32*(1-0.32)

=658.24

Take n=659

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(b)n=(Z/E)^2*p*(1-p)

=(1.65/0.03)^2*0.5*(1-0.5)

=756.25

Take n=757