7. What percentage of college students are attending a college in the state wher
ID: 3133991 • Letter: 7
Question
7. What percentage of college students are attending a college in the state where they
grew up? Let p be the proportion of college students from the same state as that
in which the college resides.
A. If no preliminary study is made to estimate p, how large a sample is needed to
be 90% sure that a point estimate p will be within a distance of 0.07 from p? 7. A. _______
(a) 139 (b) 196 (c) 340 (d) 6 (e) 138
B. A preliminary study shows that approximately 71% of college students grew up
in the same state as that in which the college resides. Answer part A using this
estimate for p. B. _______
(a) 280 (b) 113 (c) 139 (d) 114 (e) 162
Explanation / Answer
a)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.05
As there is no previous estimate for p, we set p = 0.5.
Using a table/technology,
z(alpha/2) = 1.644853627
Also,
E = 0.07
p = 0.5
Thus,
n = 138.0379313
Rounding up,
n = 139 [ANSWER, A]
**********************
b)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.05
Using a table/technology,
z(alpha/2) = 1.644853627
Also,
E = 0.07
p = 0.71
Thus,
n = 113.6880402
Rounding up,
n = 114 [answer, D]
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