Question

Reading proficiency: An educator wants to construct a 98% confidence interval for the proportion of
elementary schoolchildren in Colorado who are proficient in reading.
a. (1pt) The results of a recent statewide test suggested that the proportion is 0.70. Using this
estimate, what sample size is needed so that the confidence interval will have a margin of error
of 0.05?
b. (1pt) Estimate the sample size needed if no estimate of p is available.
c. (2pt) If the educator wanted to estimate the proportion in the entire United States rather than
in Colorado, would the necessary sample size be larger, smaller, or about the same? Explain using complete sentences

Answer 1

Solution:

The data represent reading proficiency

a)

The sample size is,

From the standard normal table ,the z-critical value at 98% confidence is 2.33

The information represent, and for finding sample size.

  

  

b)

The sample size is,

From the standard normal table ,the z-critical value at 98% confidence is 2.33

The information represent, and for finding sample size.

  

  

  

c)

If the educator wanted to estimate proportion in the entire united states rather than in Colorado,the necessary sample size is larger due to entire united states population.