Question

Compute the critical value zα/2 that corresponds to a

83​%

zα/2=_________

​(Round to two decimal places as​ needed.)

Answer 1

Solution:

Given:

c = confidence level = 83% = 0.83

then $\alpha= 1 -c= 1 - 0.83 = 0.17$

thus $\alpha / 2 = 0.17 / 2 = 0.0850$

Look in z  table for Area = 0.0850 or its closest area and find corresponding z value.

Area 0.0853 is closest to 0.0850 and it corresponds to -1.3 and 0.07

3 .00 .01 .02 .03 .04 .05 .06 .07 | .08 .09 . -3.4 .000 .000 .000 .0003 .000 .0003 .000 .00 .0003 .0002 -3.3 . .0005 .0005 .0005 0004 .0004 0004 ,0004 .00 4 .0004 ,0003 -3.2 .0007 .0007 .0006 .0006 .0006 .0006 0006 .00 5 .0005 .0005 -3.1 .0010 .0009 .0009 .0009 .0008 .0008 0008 .008 .0007 .0007 -3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .001 .0010 .0010 –2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014 -2.8 .00260025 .0024 .0023 .0023 .0022 .0021 .001 .0020 .0019 -2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .008 .0027 .0026 -2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .00380037 .0036 -2.5 .0062 .0060 .0059 .0057 .0055 .0054 0052 0051 .0049 .0048 -2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0d58 .0066 .0064 -2.3 0107 .014 01020099 .0096 .0094 0091 .089 .0087 0084 -2.2 .0139 .013601320129 .0125 .0122 .0119 .0116 .0113 .0110 -2.1 .0179 .0174 .0170 0 166 0162 .0158 0154 .05 50 .0146 .0143 -2. 0 0228 .0222 .0217 .0212 .0207 .0202.0197019 0188 .0183 -1.9 .0287 .0281 .0274 0268 .0262 .0256 .0250 .02440239 .0233 -1.8 .0359 .0351 .03440336 .0329 .0322 .03140107 .0301 .0294 -17 .0446 .04360427 . .0418.04090401 .0392.0840375 .0367 -1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .045.0465 .0455 -1.5 .06680655 .0643 0630 .0618 .0606 ,0594 ,0582 .0571 .0559 -1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .07 08 .0694 , .0681 =13 n4680951234 n91015 ਉ8 -0853 .0838 .0823

that is  z = -1.37

thus absolute z critical value= 1.37

thus

$\large \mathbf{{\color{DarkOrange} z_{\alpha / 2 } = 1.37}}$