A random sample of 5 classes taught by full-time faculty at a large university h
ID: 3158235 • Letter: A
Question
A random sample of 5 classes taught by full-time faculty at a large university have class sizes of 35, 25, 27, 30 and 40.
A. Find the mean and standard deviation of the class sizes.
B. Is there evidence that the data comes from a normal distribution? provide evidence.
C. Construct a 90% confidence interval to estimate the true mean class size for full time faculty at the university.
D. You receive a brochure from a large university. the brochure indicates that the mean class size for full time faculty is fewer than 32 students. is there enough evidence to support this claim at the x= 0.05 level?
Explanation / Answer
a)
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 157
As n = 5
Thus,
X = 31.4 [ANSWER, MEAN]
Setting up tables,
x x - X (x - X)^2
35 3.6 12.96
25 -6.4 40.96
27 -4.4 19.36
30 -1.4 1.96
40 8.6 73.96
Thus, Sum(x - X)^2 = 149.2
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 5
s^2 = 37.3
Thus,
s = 6.107372594 [ANSWER, STANDARD DEVIATION]
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b)
Yes, as there are no outliers and the values are similar to each other.
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c)
Note that
Margin of Error E = t(alpha/2) * s / sqrt(n)
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 = 31.4
t(alpha/2) = critical t for the confidence interval = 2.131846786
s = sample standard deviation = 6.107372594
n = sample size = 5
df = n - 1 = 4
Thus,
Margin of Error E = 5.822713249
Lower bound = 25.57728675
Upper bound = 37.22271325
Thus, the confidence interval is
( 25.57728675 , 37.22271325 ) [ANSWER]
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d)
No, as 32 is inside the confidence interval we have. [ANSWER, NO]
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