<PRE><B>Question 856513</B>
&amp;#967;2 = {{{( n - 1 ) * s^2 / sigma^2 = 16*(.30)^2/(.25)^2 = highlight(23.04)}}} p = .89
this &lt;u&gt;cumulative p&lt;/u&gt; just says there is an 89% chance that sample standard deviation will be &lt; .30
&lt;pre&gt;&lt;font face = &quot;Tohoma&quot; size = 3 color = &quot;indigo&quot;&gt;&lt;b&gt; 
re Reply:
Is the apparent increase in variability significant at the 0.10 level of significance? 
(.95 upper and .05 lower )  Degree of Freedom is 16
From Table:
7.962  &lt; p &lt; 26.296  , 23.04 falls in between, no not significant
Upper-tail critical values of chi-square distribution with &amp;#957; degrees of freedom  
                Probability less than the critical value
  &amp;#957;           0.90      0.95     0.975      0.99     0.999

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  1          2.706     3.841     5.024     6.635    10.828
  2          4.605     5.991     7.378     9.210    13.816
  3          6.251     7.815     9.348    11.345    16.266
  4          7.779     9.488    11.143    13.277    18.467
  5          9.236    11.070    12.833    15.086    20.515
  6         10.645    12.592    14.449    16.812    22.458
  7         12.017    14.067    16.013    18.475    24.322
  8         13.362    15.507    17.535    20.090    26.125
  9         14.684    16.919    19.023    21.666    27.877
 10         15.987    18.307    20.483    23.209    29.588
 11         17.275    19.675    21.920    24.725    31.264
 12         18.549    21.026    23.337    26.217    32.910
 13         19.812    22.362    24.736    27.688    34.528
 14         21.064    23.685    26.119    29.141    36.123
 15         22.307    24.996    27.488    30.578    37.697
 16         23.542   26.296    28.845    32.000    39.252
 17         24.769    27.587    30.191    33.409    40.790
 18         25.989    28.869    31.526    34.805    42.312

Lower-tail critical values of chi-square distribution with &amp;#957; degrees of freedom   


                Probability less than the critical value
  &amp;#957;           0.10     0.05     0.025      0.01     0.001

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  1.          .016      .004      .001      .000      .000
  2.          .211      .103      .051      .020      .002
  3.          .584      .352      .216      .115      .024
  4.         1.064      .711      .484      .297      .091
  5.         1.610     1.145      .831      .554      .210
  6.         2.204     1.635     1.237      .872      .381
  7.         2.833     2.167     1.690     1.239      .598
  8.         3.490     2.733     2.180     1.646      .857
  9.         4.168     3.325     2.700     2.088     1.152
 10.         4.865     3.940     3.247     2.558     1.479
 11.         5.578     4.575     3.816     3.053     1.834
 12.         6.304     5.226     4.404     3.571     2.214
 13.         7.042     5.892     5.009     4.107     2.617
 14.         7.790     6.571     5.629     4.660     3.041
 15.         8.547     7.261     6.262     5.229     3.483
 16.         9.312     7.962     6.908     5.812     3.942
 17.        10.085     8.672     7.564     6.408     4.416
 18.        10.865     9.390     8.231     7.015     4.905



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