document.write( "Question 856513: In the past the standard deviation of weights of certain 32.0-oz packages filled by a machine was 0.25 oz. A random sample of 17 packages showed a standard deviation of 0.30 oz. Is the apparent increase in variability significant at the 0.10 level of significance? Assume package weight is normally distributed.
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\n" ); document.write( "(ii) Find χ2. (Give your answer correct to two decimal places.) \r
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\n" ); document.write( "\n" ); document.write( "(iii) Find the p-value. (Give your answer bounds exactly.)
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Algebra.Com's Answer #516017 by ewatrrr(24785)\"\" \"About 
You can put this solution on YOUR website!
χ2 = p = .89
\n" ); document.write( "this cumulative p just says there is an 89% chance that sample standard deviation will be < .30
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document.write( "re Reply:
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document.write( "Is the apparent increase in variability significant at the 0.10 level of significance? 
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document.write( "(.95 upper and .05 lower )  Degree of Freedom is 16
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document.write( "From Table:
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document.write( "7.962  < p < 26.296  , 23.04 falls in between, no not significant
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document.write( "Upper-tail critical values of chi-square distribution with ν degrees of freedom  
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document.write( "                Probability less than the critical value
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document.write( "  ν           0.90      0.95     0.975      0.99     0.999\r
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document.write( "  1          2.706     3.841     5.024     6.635    10.828
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document.write( "  2          4.605     5.991     7.378     9.210    13.816
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document.write( "  3          6.251     7.815     9.348    11.345    16.266
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document.write( "  4          7.779     9.488    11.143    13.277    18.467
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document.write( "  5          9.236    11.070    12.833    15.086    20.515
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document.write( "  6         10.645    12.592    14.449    16.812    22.458
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document.write( "  7         12.017    14.067    16.013    18.475    24.322
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document.write( "  8         13.362    15.507    17.535    20.090    26.125
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document.write( "  9         14.684    16.919    19.023    21.666    27.877
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document.write( " 10         15.987    18.307    20.483    23.209    29.588
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document.write( " 11         17.275    19.675    21.920    24.725    31.264
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document.write( " 12         18.549    21.026    23.337    26.217    32.910
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document.write( " 13         19.812    22.362    24.736    27.688    34.528
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document.write( " 14         21.064    23.685    26.119    29.141    36.123
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document.write( " 15         22.307    24.996    27.488    30.578    37.697
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document.write( " 16         23.542   26.296    28.845    32.000    39.252
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document.write( " 17         24.769    27.587    30.191    33.409    40.790
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document.write( " 18         25.989    28.869    31.526    34.805    42.312\r
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document.write( "Lower-tail critical values of chi-square distribution with ν degrees of freedom   \r
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document.write( "                Probability less than the critical value
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document.write( "  ν           0.10     0.05     0.025      0.01     0.001\r
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document.write( "  1.          .016      .004      .001      .000      .000
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document.write( "  2.          .211      .103      .051      .020      .002
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document.write( "  3.          .584      .352      .216      .115      .024
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document.write( "  4.         1.064      .711      .484      .297      .091
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document.write( "  5.         1.610     1.145      .831      .554      .210
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document.write( "  6.         2.204     1.635     1.237      .872      .381
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document.write( "  7.         2.833     2.167     1.690     1.239      .598
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document.write( "  8.         3.490     2.733     2.180     1.646      .857
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document.write( "  9.         4.168     3.325     2.700     2.088     1.152
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document.write( " 10.         4.865     3.940     3.247     2.558     1.479
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document.write( " 11.         5.578     4.575     3.816     3.053     1.834
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document.write( " 12.         6.304     5.226     4.404     3.571     2.214
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document.write( " 13.         7.042     5.892     5.009     4.107     2.617
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document.write( " 14.         7.790     6.571     5.629     4.660     3.041
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document.write( " 15.         8.547     7.261     6.262     5.229     3.483
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document.write( " 16.         9.312     7.962     6.908     5.812     3.942
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document.write( " 17.        10.085     8.672     7.564     6.408     4.416
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document.write( " 18.        10.865     9.390     8.231     7.015     4.905\r
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