STEP - BY - STEP EXPLANATION
Whatto find?
• 90% confidence interval for the population proportion.
,
• 95% confidence interval for the ppulation proportion.
Given:
n= 800
p=0.66
q=1- p= 1- 0.66 =0.34
a) Given a 90% confidence interval,
α =1- 0.90= 0.10
[tex]Z_{\frac{\alpha}{2}}=Z_{\frac{0.10}{2}}=Z_{0.05}=1.645[/tex][tex]C.I=\bar{P}\pm Z_{\frac{\alpha}{2}}\times\sqrt{\frac{\bar{P}\bar{q}}{n}}[/tex][tex]=0.66\pm1.645\times\sqrt{\frac{0.66\times0.34}{800}}[/tex][tex]\begin{gathered} =0.66\pm0.02755 \\ \\ =(0.6324,\text{ 0.6276\rparen} \end{gathered}[/tex]
b)
Given 95% confidence interal.
1- 0.95 =0.
ANSWER
a) (0.6276, 0.6324)
