Question

Practice with Inference for Proportions Homework Name: \( \qquad \) 1. A Gallop Poll on energy use asked 512 randomly selected adults if they favored "increasing the use of nuclear power as a major source of energy". Gallop reported that 225 said "Yes". Does this poll give good evidence that fewer than half of all adults favor increased use of nuclear power? a) Find a \( 90 \% \) confidence interval for the proportion of adults who favor increased use of nuclear power. Be sure to check all assumptions. ssumptions: \[ n=512 \quad \hat{p}=\frac{205}{512}=0.4395 \] dom sample given is reasonable that the population of adults at least \( 512(10)=512 \), so our sample independent \[ \hat{p}=512(0.4395)=225.024 \quad n(1-\hat{p})=512(1-0.4395)=286.976 \] since both are \( >10 \), the distribution of \( \hat{p} \) is is normal \[ \left(\frac{225}{512}\right)+1.65 \sqrt{\frac{0.4395(1-0.4395)}{512}} \] we are \( 90 \% \) confident that: \( 0.4034 \leq P \leq 0.4755 \) b) Conduct a Hypothesis Test to determine if the proportion of adults who favor increased use of nuclear power is less than \( 50 \% \). Check all assumptions and use \( \alpha=0.05 \). \( H_{0}= \)

          Practice with Inference for Proportions Homework

Name: \( \qquad \)
1. A Gallop Poll on energy use asked 512 randomly selected adults if they favored "increasing the use of nuclear power as a major source of energy". Gallop reported that 225 said "Yes". Does this poll give good evidence that fewer than half of all adults favor increased use of nuclear power?
a) Find a \( 90 \% \) confidence interval for the proportion of adults who favor increased use of nuclear power. Be sure to check all assumptions.
ssumptions:
\[
n=512 \quad \hat{p}=\frac{205}{512}=0.4395
\]
dom sample given
is reasonable that the population of adults
at least \( 512(10)=512 \), so our sample
independent
\[
\hat{p}=512(0.4395)=225.024 \quad n(1-\hat{p})=512(1-0.4395)=286.976
\]
since both are \( >10 \), the distribution of \( \hat{p} \) is is normal
\[
\left(\frac{225}{512}\right)+1.65 \sqrt{\frac{0.4395(1-0.4395)}{512}}
\]
we are \( 90 \% \) confident that:
\( 0.4034 \leq P \leq 0.4755 \)
b) Conduct a Hypothesis Test to determine if the proportion of adults who favor increased use of nuclear power is less than \( 50 \% \). Check all assumptions and use \( \alpha=0.05 \).
\( H_{0}= \)

Practice with Inference for Proportions Homework

Name:
1. A Gallop Poll on energy use asked 512 randomly selected adults if they favored "increasing the use of nuclear power as a major source of energy". Gallop reported that 225 said "Yes". Does this poll give good evidence that fewer than half of all adults favor increased use of nuclear power?
a) Find a 90 % confidence interval for the proportion of adults who favor increased use of nuclear power. Be sure to check all assumptions.
ssumptions:

n=512 p̂=(205)/(512)=0.4395

dom sample given
is reasonable that the population of adults
at least 512(10)=512, so our sample
independent

p̂=512(0.4395)=225.024 n(1-p̂)=512(1-0.4395)=286.976

since both are >10, the distribution of p̂ is is normal

((225)/(512))+1.65 √((0.4395(1-0.4395))/(512))

we are 90 % confident that:
0.4034 ≤ P ≤ 0.4755
b) Conduct a Hypothesis Test to determine if the proportion of adults who favor increased use of nuclear power is less than 50 %. Check all assumptions and use α=0.05.
H0=

Added by Lisa B.

Question

Please give Ace some feedback