Question

A new batching plant has been constructed and of the first 50 batches, three are found to not meet specification. a. Construct a 98% Score confidence interval for the population proportion of batches that do not meet specification for the new batching plant. b. Construct a 98% traditional confidence interval.c. Comment on the difference.

Answer 1

The responses to these question can be defined as follows:

Explanation:

`x=3 \\\\n=50\\\\\hat{p}=(x)/(n)=0.06\\\\\hat{q}=1-\hat{p}=0.94`

In point a:

`98\%` confidence interval for population proportion (p):

`c=98\%=0.98\\\\\alpha=1-c=0.02\\\\(\alpha)/(2)=(0.02)/(2)=0.01\\\\z_{(\alpha)/(2)}=2.326\\\\`

For point b:

`98\% \ confidence\ interval =\hat{p} \pm z_{(\alpha)/(2)} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\`

`=0.06 \pm 2.326 \sqrt{(0.06* 0.94)/(50)}\\\\ =0.06 \pm 2.326 (0.0336)\\\\=0.06 \pm 0.078\\\\98\% \ CI =(-0.018, 0.138)`

For point c:

`The\ difference\ between \ 98\% \ CI\ is \ -0.018\ to\ 0.138`