An education professor is interested in estimating thepercentage of freshman stu

Question

An education professor is interested in estimating thepercentage of freshman students that work fulltime while attendingcollege.

a.       The professor wants toconstruct 99% Confidence Interval while only allowing for 3% error.Assuming no prior estimates are available, how large of a sampleshould she collect?

b.      Due to funding shortages,the professor is only able to gather a random sample of 500students. She discovers that 205 of these 500 students workfulltime while attending school. Using this information, constructa 99% confidence interval for the proportion of students that workfulltime while attending school.

c.       The professorbelieves that 40% of freshman work full-time. At = 0.05level of significance and the data listed in part b, use a 5-stephypothesis test to determine if there enough evidence to supportthe professor’s claim.

Please help me I am so lost.

Looking forward to your kind advice

Thanks

Explanation / Answer

(a) Given =0.01, Z(0.005)=2.58 (check normal table) E=0.03 n=(Z/E)^2*p*(1-p) =(2.58/0.03)^2*0.5*0.5 =1849 (b) n=500, phat=205/500 =0.41 The 99% CI is phat ± Z*phat*(1-phat)/n --> 0.41 ± 2.58*sqrt(0.41*(1-0.41)/500) --> (0.353, 0.467) (c) =0.05, Z(0.025)=1.96 (check normal table) The test hypothesis is Ho:p=0.4 Ha:p not equal 0.4 The test statistic is Z=(phat-p)/p*(1-p)/n =(0.41-0.4)/sqrt(0.4*(1-0.4)/500) =0.46 Since Z=0.46

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