Question

A sample of 17 items was taken, and 5 of the units were found to be green. What is the 97% upper confidence limit(one-sided) for the percentage of green items

Answer 1

The 97% upper confidence limit for the proportion of green items is 0.502.

Explanation:

We have to calculate a 97% upper confidence limit for the proportion.

The sample proportion is p=0.294.

`p=X/n=5/17=0.294\\`

The standard error of the proportion is:

`\sigma_p=\sqrt{(p(1-p))/(n)}=\sqrt{(0.294*0.706)/(17)}\\\\\\ \sigma_p=√(0.01221)=0.11`

The critical z-value for a 97% upper confidence limit is z=1.881.

The margin of error (MOE) can be calculated as:

`MOE=z\cdot \sigma_p=1.881 \cdot 0.11=0.208`

Then, the upper bound is:

`UL=p+z \cdot \sigma_p = 0.294+0.208=0.502`

The 97% upper confidence limit for the proportion of green items is 0.502.