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Lerok [7]
3 years ago
9

Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a

confidence level of 98%, and use the results from a prior Harris poll that gave a confidence interval of (0.44, 0.51) for the proportion of Democrats who have a sibling.
Mathematics
1 answer:
Brums [2.3K]3 years ago
6 0

Answer:

The minimum sample size is  n  =135

Step-by-step explanation:

From the question we are told that

   The confidence interval is ( lower \ limit  = \  0.44,\ \ \   upper \ limit  = \ 0.51)

    The margin of error is  E =  0.1

   

Generally the sample  proportion can be mathematically evaluated as

     \r p = \frac{ upper \ limit  + lower \ limit }{2}

    \r p = \frac{ 0.51 + 0.44}{2}

    \r p = 0.475

Given that the confidence level is  98% then the level of significance can be mathematically evaluated as

         \alpha = 100 -  98

        \alpha = 2\%

        \alpha =0.02

Next we obtain the critical value of  \frac{\alpha }{2} from the normal distribution table  

   The value is

        Z_{\frac{\alpha }{2} } =  2.33

Generally the minimum sample size is evaluated as

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

     n  =[ \frac { 2.33}{0.1} ]^2 *  0.475(1- 0.475 )

     n  =135

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