The National Center for Education Statistics (NCES) is interested in an average
ID: 3218077 • Letter: T
Question
The National Center for Education Statistics (NCES) is interested in an average length of time it takes college students to earn their bachelor’s degree.
From previous experience, NCES believes that a Standard Deviation of a length of time is 1.68 years.
A: In a random sample of 75 college graduates an average length of time is 5.25 years.
What is a 90% Confidence Interval for an average length of time it takes college students to earn their bachelor's degree?
a. (4.80, 5.70) years
b. (4.93, 5.57) years
c. (4.87, 5.63) years
d. None of the above
B: In case 28 college graduates are chosen at random and their average length of time is 4.42 years,
find a 95% Confidence Interval for an average length of time it takes college students to earn their bachelor's degree.
a. (3.60, 5.24) years
b. (3.80, 5.04) years
c. (3.90, 4.94) years
d. None of the above
C: A random sample of 64 students yields an average length of time of 4.96 years.
Construct a 98% Confidence Interval for an average length of time it takes college students to earn their bachelor's degree.
a. (4.47, 5.45) years
b. (4.55, 5.37) years
c. (4.61, 5.31) years
d. None of the above
Explanation / Answer
A. Here n=75 so we will take z=1.645 for z
Hence E=z*sd/sqrt(n)=0.32
So CI=5.25+/-0.32=(4.93,4.47) b is answer
B. Here n=28<30 so we will use t table
t table value for n=28 is 2.052
So E=2.052*1.68/sqrt(28)=0.65
Hence CI=4.42+/.0.65=(3.77,5.07) so answer is d none of the above
c. n=64 so z=2.33
E=2.33*1.68/sqrt(64)=0.49
Hence CI=4.96+/-.49=(4.47,5.45) so a is answer
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