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]
=> [tex]\frac{s_2}{s_1} = \sqrt{\frac{n_1}{n_2} }[/tex]
=> [tex]\frac{n_1}{n_2} =[\frac{s_2}{s_1} ]^2[/tex]
=> [tex]\frac{73}{n_2} =[\frac{0.047}{0.098} ]^2[/tex]
=> [tex]\frac{73}{n_2} =0.2300[/tex]
=> [tex]n_2 = \frac{73}{0.2300}[/tex]
=> [tex]n_2 = 317[/tex]
