The lower bound is , and the upper bound is . Students taking multiple-choice te
ID: 3133799 • Letter: T
Question
The lower bound is , and the upper bound is .
Students taking multiple-choice tests sometimes find themselves reading questions whose answers they don't know. Sometimes, students can eliminate one or more of the alternative choices based on knowledge they have, or on the way the question is written, and so forth. Because of this, they tend to do better on such questions than they would if they had to select an answer at random.A multiple-choice exam consists of 50 questions, for which each has four alternatives from which the student must choose. A group of teachers has found that on similar tests, the proportion of questions correctly answered by students (when they don't know the answer) is 0.429. Please use this information to answer Questions 19 and 20.
Explanation / Answer
19.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.6
u = mean = p = 0.429
s = standard deviation = sqrt(p(1-p)/n) = 0.069994143
Thus,
z = (x - u) / s = 2.443061571
Thus, using a table/technology, the right tailed area of this is
P(z > 2.443061571 ) = 0.007281626 [ANSWER]
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20.
We first get the z score for the critical value. As z = (x - u) / s, then as
x = critical value = 0.5
u = mean = p = 0.429
s = standard deviation = sqrt(p(1-p)/n) = 0.069994143
Thus,
z = (x - u) / s = 1.014370594
Thus, using a table/technology, the left tailed area of this is
P(z < 1.014370594 ) = 0.844797025 [ANSWER]
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