Answer:
The value  is  [tex]n_2  = 317[/tex]
Step-by-step explanation:
From the question we are told that
 The sample size is  n  =  73
  The proportion that in favor of raising the tuition is  [tex]\^{p} =  0.37[/tex]
  The standard deviation is  [tex]s_1  = 0.098[/tex]
  The required standard deviation  [tex]s_2  = 0.047[/tex]
Generally the requires standard deviation is mathematically represented as
   [tex]s_2  = s_1 *  \sqrt{\frac{n_1}{n_2} }[/tex]
=> Â Â [tex]\frac{s_2}{s_1} Â = Â \sqrt{\frac{n_1}{n_2} }[/tex]
=> Â Â [tex]\frac{n_1}{n_2} =[\frac{s_2}{s_1} ]^2[/tex]
=> Â Â [tex]\frac{73}{n_2} =[\frac{0.047}{0.098} ]^2[/tex]
=> Â Â [tex]\frac{73}{n_2} =0.2300[/tex]
=> Â Â [tex]n_2 = Â \frac{73}{0.2300}[/tex]
=> Â [tex]n_2 Â = 317[/tex]
