Problem 3 : In sample of 200 economists, 147 choose the FRED database as the mos

Question

Problem 3 :

In sample of 200 economists, 147 choose the FRED database as the most popular economic database. Calculate the margin of error for a 97% confidence interval.

Calculate the lower bound for a 97% confidence interval.

ALSO:

A previous survey reported that 53% of respondents increased their portfolio value over the past 3 years. How large should a sample be if the margin of error is .03 for a 91% confidence interval?

Suppose you want to investigate the proportion of women police officers. How large should a sample be if the margin of error is .05 for a 92% confidence interval?

Explanation / Answer

1)here estimated proportion p=147/200=0.735

therefore std error=(p(1-p)/n)1/2 =0.0312

for 97% CI ; critical value of z =2.17

hence  margin of error for a 97% confidence interval =z*std error =0.0677

lower bound for a 97% confidence interval =sample proportion -margin of error =0.6673

2)

for p=0.53

margin of error E =0.03

for a 91% CI ; z =1.6954

hence required sample size n=p(1-p)*(Z/E)2 =~ 796

(ii)

for no estimate p=0.5

margin fo error E =0.05

for a 92% CI ; z =1.7507

required sample size n=p(1-p)*(Z/E)2 =~307

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