To become an actuary, it is necessary to pass a series of 10 exams, including th
ID: 3155150 • Letter: T
Question
To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and mean of the sample is 6 while the standard deviation of this sample is 2.
a) Construct a 90% confidence interval for the mean score of actuarial students in the special program.
b) What is point of estimate?
Explanation / Answer
a.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=6
Standard deviation( sd )=2
Sample Size(n)=8
Confidence Interval = [ 6 ± t a/2 ( 2/ Sqrt ( 8) ) ]
= [ 6 - 1.895 * (0.707) , 6 + 1.895 * (0.707) ]
= [ 4.66,7.34 ]
b.
Point of estimate = mean score of actuarial students = Mean rate = 6
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