MTH 380
Assignment # 4
Fall 2023
NOTE: Please submit your answers in a PDF file in ”Assessment → Assignment
4” on the common course shell before the deadline. Penalty for late submission is
50% your marks.
Problem 1.
a) The following sample has been taken from a normal distribution with
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variance σ = 1 and unknown mean µ.
−0.7518, 1.4977, 1.7274, 1.8371, −0.3193, 0.7773, 1.0900, 0.7659, 0.3623, 1.7205
Find a 95% confidence interval for µ?What is the length of the interval?
b) What sample size should be used to obtain a 95% confidence interval for µ of length
0.5 in question (a)?
Problem 2. The wall thickness of 25 glass 2-liter bottles was measured by a quality controlengineer. The sample mean was x̄ = 4.05 millimeters, and the sample standard deviation was
s = 0.08. The probability plot for this sample support the assumption that the population is
normally distributed. Find a 95% lower confidence bound for mean wall thickness.
Problem 3. The percentage of titanium in an alloy used in aerospace castings is measured
in 51 randomly selected parts. The sample standard deviation is s = 0.37 and the probability
plot support the assumption that the population is normally distributed. Construct a 95%
two-sided confidence interval for σ.
Problem 4. A consumer products company is formulating a new shampoo and is interested
in foam height (in millimeters). Foam height is approximately normally distributed and has a
standard deviation of 20 millimeters. The company wishes to test H0 : µ = 175 millimeters vs
H1 : µ > 175 millimeters, using the results of n = 10 samples.
a) Find the type I error probability α if the critical region is x̄ > 185.
b) Find the boundary point of the acceptance region if α = 0.05.
Problem 5. The temperatures of female monkeys follow a normal distribution. A sample is
as follows: 97.8, 97.2, 97.4, 97.6, 97.8, 97.9, 98.0, 98.0, 98.0, 98.1, 98.2, 98.3, 98.3, 98.4, 98.4,
98.4, 98.5, 98.6, 98.6, 98.7, 98.8, 98.8, 98.9, 98.9, 99.0.
a) Find the sample size, mean and standard deviation.
b) Test the hypothesis H0 : µ = 98.6 versus H1 : µ 6= 98.6, using α = 0.05. Find the
P-value.
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