Use the given degree of confidence and sample data to construct a confidence int
ID: 3132525 • Letter: U
Question
Use the given degree of confidence and sample data to construct a confidence interval for the population mean . Assume that the population has a normal distribution.
The principal randomly selected six students to take an aptitude test. Their scores were:
77.2 75.1 85.6 81.3 88.4 77.4
Determine a 90% confidence interval for the mean score for all students.
74.99 < < 83.28
76.51 < < 85.16
83.28 < < 74.99
83.38 < < 74.89
74.99 < < 83.28
76.51 < < 85.16
83.28 < < 74.99
83.38 < < 74.89
Explanation / Answer
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 80.83333333
t(alpha/2) = critical t for the confidence interval = 2.015048373
s = sample standard deviation = 5.254585299
n = sample size = 6
df = n - 1 = 5
Thus,
Lower bound = 76.510701
Upper bound = 85.15596567
Thus, the confidence interval is
( 76.51 , 85.16 ) [ANSWER, B]
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