MATH 380 Dan iel W r ight S. Gom ez
Applied Statistics W ith Solution s +
r ation ales ( 2025 latest r elease )
MATH 380 | August 23, 2025
Daniel Wright
S. Gomez
MATH 380
Applied Statistics
With Solutions
Problem 1: A researcher collected the following data on
customer satisfaction scores: 122.1,
90.3, 123.1, 97.6, 89.6, 87.8, 92.3, 114.1, 95.9, 84.2, 109.4,
102, 103.2, 74.2, 87.1, 97, 138.2, 103.5, 83.1, 107 Calculate:
a) The sample mean b) The sample standard deviation c) The
median and quartiles d) Interpret the results in context
, Solution:
Solution:
a) Sample mean
( ):x̄ x̄ = Σx/n =
2001.7/20 = 100.09
b) Sample
standard deviation
(s):s = √[Σ(x - )²/(n-1)]
= 15.65x̄ c) Median
and quartiles:
Ordered data: 74.2, 83.1, 84.2, 87.1, 87.8, 89.6, 90.3, 92.3,
95.9, 97, 97.6, 102, 103.2, 103.5, 107, 109.4, 114.1, 122.1,
123.1, 138.2
Median (Q2) = 97.3
Q1 =
89.6 Q3
= 109.4
d) Interpretation:
The average satisfaction score is 100.09, with moderate
variability (s = 15.65).
50% of scores fall between 89.6 and 109.4.
Problem 2: A company claims their average delivery time is
54 minutes. A sample of 36 deliveries shows a mean of 48.6
minutes with a standard deviation of 11.4 minutes. Test at α
= 0.05 level: H₀: μ = 54 H₁: μ ≠ 54 a) Calculate the test statistic
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Applied Statistics W ith Solution s +
r ation ales ( 2025 latest r elease )
MATH 380 | August 23, 2025
Daniel Wright
S. Gomez
MATH 380
Applied Statistics
With Solutions
Problem 1: A researcher collected the following data on
customer satisfaction scores: 122.1,
90.3, 123.1, 97.6, 89.6, 87.8, 92.3, 114.1, 95.9, 84.2, 109.4,
102, 103.2, 74.2, 87.1, 97, 138.2, 103.5, 83.1, 107 Calculate:
a) The sample mean b) The sample standard deviation c) The
median and quartiles d) Interpret the results in context
, Solution:
Solution:
a) Sample mean
( ):x̄ x̄ = Σx/n =
2001.7/20 = 100.09
b) Sample
standard deviation
(s):s = √[Σ(x - )²/(n-1)]
= 15.65x̄ c) Median
and quartiles:
Ordered data: 74.2, 83.1, 84.2, 87.1, 87.8, 89.6, 90.3, 92.3,
95.9, 97, 97.6, 102, 103.2, 103.5, 107, 109.4, 114.1, 122.1,
123.1, 138.2
Median (Q2) = 97.3
Q1 =
89.6 Q3
= 109.4
d) Interpretation:
The average satisfaction score is 100.09, with moderate
variability (s = 15.65).
50% of scores fall between 89.6 and 109.4.
Problem 2: A company claims their average delivery time is
54 minutes. A sample of 36 deliveries shows a mean of 48.6
minutes with a standard deviation of 11.4 minutes. Test at α
= 0.05 level: H₀: μ = 54 H₁: μ ≠ 54 a) Calculate the test statistic
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