The research department in the US Department of Education statesthat 55% of curr
ID: 2954878 • Letter: T
Question
The research department in the US Department of Education statesthat 55% of current college students are planning to attendgraduate school based on its reliable resource and extensiveresearch.(a). A University dean is interested in determining the proportionof students who are planning to attend graduate school. Rather thanexamine the records for all students, the dean randomly selects 200students and finds that 118 of them are planning to attend graduateschool. Find a 99% confidence interval for the true populationproportion of the students who are planning to attend graduateschool. Interpret the result; use the z-score with the accuratethird decimal place.
(b). Based on the interval in part (a)., can this dean be 99%confident that more than 70% of the students are planning to attendgraduate school (yes/no and explain)?
(c). Determine the sample size needed in order to be 95% confidentthat the sample proportion of students who plan to attend graduateschool is within .03 of p, the true proportion of students who planto attend graduate school. Interpret the result and state which pyou should use and why.
(d). Without any calculation, how would the sample size in part(c). change if we change from 95% confidence to 99% confidence withall other considerations being kept the same? How about change to90%?
For 99%: More samples needed OR Less samples Needed
For 90%: More samples needed OR Less samples Needed
Explanation / Answer
Given p=0.55 (a) Given n=200, phat=118/200 =0.59, =0.01, Z(0.005)=2.58 (check normal tabl) The 99% CI is phat ± Z*p*(1-p)/n --> 0.59 ± 2.58*sqrt(0.55*(1-0.55)/200) --> (0.4992, 0.6807) z-score= (phat-p)/p*(1-p)/n =(0.59-0.55)/sqrt(0.55*(1-0.55)/200) =1.14 (b) No, this interval does not include 70%. (c) Given =0.05, Z(0.025)=1.96 (check normal table) E=0.03 n=(Z/E)^2*p*(1-p) where p is unknown =(1.96/0.03)^2*0.5*0.5 =1067.111 Take n=1068 (d) For 99%: More samples needed For 90%: Less samples Needed