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harina [27]
3 years ago
11

A survey of 73 students found that 37% were in favor of raising tuition to pave new parking lots. The standard deviation of the

sample proportion is 9.8%. How large a sample (to the nearest person) would be required to reduce this standard deviation to 4.7%?
Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

The value  is   n_2  = 317

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  \^{p} =  0.37

   The standard deviation is  s_1  = 0.098

    The required standard deviation  s_2  = 0.047

Generally the requires standard deviation is mathematically represented as

      s_2  = s_1 *  \sqrt{\frac{n_1}{n_2} }

=>    \frac{s_2}{s_1}  =  \sqrt{\frac{n_1}{n_2} }

=>    \frac{n_1}{n_2} =[\frac{s_2}{s_1} ]^2

=>     \frac{73}{n_2} =[\frac{0.047}{0.098} ]^2

=>     \frac{73}{n_2} =0.2300

=>     n_2 =  \frac{73}{0.2300}

=>   n_2  = 317

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The first equation is confirmed. Let's check the second equation

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