Section 9.1 Learning Check|&lt;b&gt;Please refer to the following explanation for the questions 1-4.&lt;br&gt; Noether (Mental Random Numbers:Perceived and Real Randomness, &lt;u&gt;Teaching Statistics&lt;/u&gt;, 1987) asked students as random pairs from the digits 1, 2, 3, repeating that process four times. Noether recorded frequency of occurrences of the last digit pair written down by each of 450 students. The results were: &lt;br&gt;&lt;br&gt;&lt;center&gt;&lt;table border=1 cellspacing=0 cellpadding=0 style='border-collapse:collapse;  border:none;mso-border-alt:solid windowtext .5pt;mso-padding-alt:0in 5.4pt 0in 5.4pt'&gt;  &lt;tr&gt;   &lt;td width=192 colspan=2 rowspan=2 valign=top style='width:191.5pt;border:   solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal&gt;&lt;![if !supportEmptyParas]&gt; &lt;![endif]&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;   &lt;/td&gt;   &lt;td width=287 colspan=3 valign=top style='width:287.3pt;border:solid windowtext .5pt;   border-left:none;mso-border-left-alt:solid windowtext .5pt;background:KPHHASHFFFF99;   padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;First Digit&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHFFFF99;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;1&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHFFFF99;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;2&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.8pt;border-top:none;border-left:none;   border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHFFFF99;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;3&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td width=96 rowspan=3 valign=top style='width:95.75pt;border:solid windowtext .5pt;   border-top:none;mso-border-top-alt:solid windowtext .5pt;background:KPHHASHCCFFFF;   padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal&gt;&lt;![if !supportEmptyParas]&gt; &lt;![endif]&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/p&gt;   &lt;p class=MsoNormal&gt;Second Digit&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFFF;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;1&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;31&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;72&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.8pt;border-top:none;border-left:none;   border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;60&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFFF;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;2&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;57&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;27&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.8pt;border-top:none;border-left:none;   border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;63&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt;  &lt;tr&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFFF;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;3&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;53&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.75pt;border-top:none;border-left:   none;border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;58&lt;/p&gt;   &lt;/td&gt;   &lt;td width=96 valign=top style='width:95.8pt;border-top:none;border-left:none;   border-bottom:solid windowtext .5pt;border-right:solid windowtext .5pt;   mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;   background:KPHHASHCCFFCC;padding:0in 5.4pt 0in 5.4pt'&gt;   &lt;p class=MsoNormal align=center style='text-align:center'&gt;29&lt;/p&gt;   &lt;/td&gt;  &lt;/tr&gt; &lt;/table&gt;    &lt;/center&gt;&lt;/b&gt;|Please enter your Full Name:|Your Email Address:|Your ID Number or Password:|This is an <b>r</b>x<b>c</b> table. The number <b>r</b> has value # 1 %% 2 %% 3 %% 4 %%|Which null hypothesis are being tested by the chi-square test for this problem? # There is an association between the first and second digits. %% There is no association between first and second digits. %% The average value for the second digit is the same for all first digits. %% The average value of the second digit is different for all first digits. %%|The expected cell count for the cell in which the first digit is 2 and the second digit is 2 is # 63.00 %% 27.00 %% 56.87 %% 51.29 %%|The value of the Chi-square test statistic is 40.7368. Which of the following may we conclude? # There is strong evidence of an association between the first and second digits. %% There is no evidence of association between first and second digits. %% There is no evidence that the distribution of the second digit is the same for each value of the first digit. %% The distribution for the first digit is the same as second digit. %%