Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
ANSWER:
Lower limit: 0.77
Upper limit: 0.84
STEP-BY-STEP EXPLANATION:
Given:
x = 303
n = 375
We calculate the value of the proportion in the following way:
[tex]\begin{gathered} p=\frac{x}{n}=\frac{303}{375} \\ \\ p=0.808 \end{gathered}[/tex]For a 90% confidence interval we have the following:
[tex]\begin{gathered} \alpha=100\%-90\%=10\%=0.1 \\ \\ \alpha\text{/2}=0.1=0.05 \\ \\ \text{ For the normal table this corresponds to:} \\ \\ Z_{\alpha\text{/2}}=1.645 \end{gathered}[/tex]We calculate the limits of the 90% confidence interval using the following formula:
[tex]\begin{gathered} \text{ Lower limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot(1-p)}{n}}=\:0.808-1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}\:=0.77 \\ \\ \:\text{Upper limit: }p-Z_{\alpha\text{/2}}\cdot\sqrt{\frac{p\cdot\left(1-p\right)}{n}}\:=0.808+1.645\cdot\sqrt{\frac{0.808\cdot\left(1-0.808\right)}{375}}=0.84 \end{gathered}[/tex]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.