Answer:
The 97% upper confidence limit for the proportion of green items is 0.502.
Step-by-step explanation:
We have to calculate a 97% upper confidence limit for the proportion.
The sample proportion is p=0.294.
[tex]p=X/n=5/17=0.294\\[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.294*0.706}{17}}\\\\\\ \sigma_p=\sqrt{0.01221}=0.11[/tex]
The critical z-value for a 97% upper confidence limit is z=1.881.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208[/tex]
Then, the upper bound is:
[tex]UL=p+z \cdot \sigma_p = 0.294+0.208=0.502[/tex]
The 97% upper confidence limit for the proportion of green items is 0.502.
