A new batching plant has been constructed and of the first 50 batches, three are found to not meet specification. a. Construct a 98% Sco

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.

in progress 0
Thu Hương 3 months 2021-08-21T23:26:14+00:00 1 Answers 1 views 0

Answers ( )

    0
    2021-08-21T23:27:33+00:00

    Answer:

    The responses to these question can be defined as follows:

    Step-by-step explanation:

    x=3 \\\\n=50\\\\\hat{p}=\frac{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\\\\\frac{\alpha}{2}=\frac{0.02}{2}=0.01\\\\z_{\frac{\alpha}{2}}=2.326\\\\

    For point b:

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

                                            =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)

    For point c:

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

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )