A Social service agency plans to conduct a survey to determine the mean income of its clients. The director of the agency prefers that you measure the mean income very accurately, to within plus or minus $500. from a sample taken 2 years ago, you estimate that the standard deviation of income for this population is about $5000. I need to figure out the necessary sample size to reduce the confidence interval to plus/minus$500

the necessary sample size to reduce the confidence interval to plus/minus$500 is

Step-by-step explanation:

We are given from the question that

          Marginal error E = $500

        The standard deviation is = $5000

        Let the level of significance be

In order to obtain the sample size n we make use of formula

 Now   is the Z score of /2 and this can be obtained from the z-table and from the z table the  z - score for this case of level of significance  is 1.96

  Substituting value into the formula above

step-by-step explanation:

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