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Reika [66]
3 years ago
9

Minnesota Public Radio wants to duplicate a survey conducted in 2016 that found that 65% of adults living in Minnesota felt that

the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%? (You must show the formula and your algebraic work to receive credit for this problem.)
Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0

Answer:

The number of people needed  is n =684  

Step-by-step explanation:

From the question we are told that

  The population proportion is  p = 0.65

   The margin of error is  E = 0.03

From the question we are told the confidence level is  90% , hence the level of significance is    

      \alpha = (100 - 90 ) \%

=>   \alpha = 0.10

Generally from the normal distribution table the critical value  of  \frac{\alpha }{2} is  

   Z_{\frac{\alpha }{2} } =  1.645

Generally the sample size is mathematically represented as

       n =[ \frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * p(1-p)

=>    n =[ \frac{1.645 }{0.03} ]^2 * 0.65(1-0.65)

=>    n =684  

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