la) Reading in a survey of 700 community co e students, 4si indicated that they

Question

la) Reading in a survey of 700 community co e students, 4si indicated that they have read a during the school year (based on data from the Community College Survey of Student Engagement). read Calculate a point estimate of the proportion p of community college students who have for personal enjoyment during the school year. Determine if the sample satisfies the conditions for constructing a confidence interval for p. Determine the appropriate critical value for a 94% confidence interval for p Construct and interpret a 94% confidence interval for p. 1b) Using your point estimate from (la) as a prior estimate of p, how large of a sample would be required to estimate p to within 1.5%, with 94% confidence.

Explanation / Answer

Solution:

1a) Given that X = 481 and n = 700

Using Z-tables, the critical value is

Z (0.06/2) = Z (0.03) = 1.881

p ± Z (a/2)* p (1 – p)/n

0.687 ± 1.881*0.687*(1 – 0.687)/700

0.687 ± 1.881*0.0175

0.687 ± 0.033

0.687 – 0.033, 0.687 + 0.033

0.654, 0.72

1b) The sample size is given by:-

N = [Z/E]^2*p*(1 – p)

N = [1.881/0.015]^2*0.687*(1-0.687)

N = 15725.16*0.687*0.313

N = 3381.4

N = 3382

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