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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]
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