Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Answer:
The responses to these question can be defined as follows:
Step-by-step explanation:
[tex]x=3 \\\\n=50\\\\\hat{p}=\frac{x}{n}=0.06\\\\\hat{q}=1-\hat{p}=0.94[/tex]
In point a:
[tex]98\%[/tex] confidence interval for population proportion (p):
[tex]c=98\%=0.98\\\\\alpha=1-c=0.02\\\\\frac{\alpha}{2}=\frac{0.02}{2}=0.01\\\\z_{\frac{\alpha}{2}}=2.326\\\\[/tex]
For point b:
[tex]98\% \ confidence\ interval =\hat{p} \pm z_{\frac{\alpha}{2}} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\[/tex]
[tex]=0.06 \pm 2.326 \sqrt{\frac{0.06\times 0.94}{50}}\\\\ =0.06 \pm 2.326 (0.0336)\\\\=0.06 \pm 0.078\\\\98\% \ CI =(-0.018, 0.138)[/tex]
For point c:
[tex]The\ difference\ between \ 98\% \ CI\ is \ -0.018\ to\ 0.138[/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
