Question

1. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 91% C.L. for the proportion of adults who favor the “legal marriage” position.

2. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 94% C.L. for the proportion of adults who favor the “civil union” position.

3. A survey about same-sex marriage used a random sample with 1200 adults. The results showed that 30% favored legal marriage, 32% favored civil unions, and 38% favored no legal recognition. Computer the right boundary at the 97% C.L. for the proportion of adults who favor the “no legal recognition” position.

Answer 1

a)

sample proportion, = 0.3
sample size, n = 1200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.3 * (1 - 0.3)/1200) = 0.0132

Given CI level is 91%, hence α = 1 - 0.91 = 0.09
α/2 = 0.09/2 = 0.045, Zc = Z(α/2) = 1.7

Margin of Error, ME = zc * SE
ME = 1.7 * 0.0132
ME = 0.0224

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.3 - 1.7 * 0.0132 , 0.3 + 1.7 * 0.0132)
CI = (0.2776 , 0.3224)

Right Boundary = 0.3224

b)

sample proportion, = 0.32
sample size, n = 1200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.32 * (1 - 0.32)/1200) = 0.0135

Given CI level is 94%, hence α = 1 - 0.94 = 0.06
α/2 = 0.06/2 = 0.03, Zc = Z(α/2) = 1.88

Margin of Error, ME = zc * SE
ME = 1.88 * 0.0135
ME = 0.0254

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.32 - 1.88 * 0.0135 , 0.32 + 1.88 * 0.0135)
CI = (0.2946 , 0.3454)

right boundary = 0.3454

c)

sample proportion, = 0.38
sample size, n = 1200
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.38 * (1 - 0.38)/1200) = 0.014

Given CI level is 97%, hence α = 1 - 0.97 = 0.03
α/2 = 0.03/2 = 0.015, Zc = Z(α/2) = 2.17

Margin of Error, ME = zc * SE
ME = 2.17 * 0.014
ME = 0.0304

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.38 - 2.17 * 0.014 , 0.38 + 2.17 * 0.014)
CI = (0.3496 , 0.4104)

right boundary = 0.4104