As part of a study of high school graduates in Providence, to be carried out by

Question

As part of a study of high school graduates in Providence, to be carried out by URI, a random sample of graduating students is to be selected to estimate the proportion of those who expect to enter the labor force upon graduation. It is desirable to estimate the population proportion with a margin of error of 5% and a 90 percent level of confidence. No reliable value for p is available.

a) What sample size will be large enough to ensure that the estimate has the desired precision? (5 pts.)

b) If the University officials are interested in calculating the proportion of students going into the labor force with a margin of error of 10% and the same level of confidence as in part (a), would you expect the sample size to increase, decrease or stay the same? Explain. (4 pts.)

c) It was finally decided to include 150 students in the study. Of these, 65 stated that they expect to enter the labor force upon graduation. i. Find a point estimate of the proportion of students that expect to enter the labor force upon graduation. (5 pts.)

d) Construct a 90% confidence interval for the population proportion. (6 pts.)

Explanation / Answer

a) here margin or error E=0.05

for no estimated proportion; p=0.5

for 90% CI, z=1.645

ehnce sample size n=p(1-p)*(z/E)2  =~271

b)as margin of error increases sample size decrease due to both are inversely proportional

c)point estimate p=65/150 =0.433

hence std error =(p(1-p)/n)1/2 =0.0405

for confidence interval =p -/+ z*std error =0.3668 ; 0.4999

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