CMTH 380
Assignment
#
4
Winter 2024
DUE: on D2L at 11:59 pm April 12, 2024
NOTE: Please submit your answers in a PDF file in ”Assessment
→
Assignment
4” on the course shell before the deadline. Penalty for late submission is 50% your
marks.
Problem 1.
The following sample has been taken from a normal distribution with variance
σ
2
= 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
a) 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.
A melting point test of
n
= 10 samples of a binder used in manufacturing a rocket
propellant resulted in ¯
x
= 154
.
2
o
F
.
Assume that the melting point is normally distributed
with
σ
= 1
.
5
o
F
. Test
H
0
:
µ
= 155 versus
H
1
:
µ
̸
= 155 using
α
= 0
.
01.
(a) Find the acceptance region.
(b) Find the P-value for this test.
(c) Make a conclusion.
Problem 3.
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.
n
= 25
¯
x
=
∑
25
i
=1
x
i
25
= 98
.
264
s
2
=
∑
25
i
=1
(
x
i
−
¯
x
)
2
25
−
1
= 0
.
2324
b) Test the hypothesis
H
0
:
µ
= 98
.
6 versus
H
1
:
µ
̸
= 98
.
6, using
α
= 0
.
05.
Find the
P-value.
Problem 4.
The wall thickness of 25 glass 2-liter bottles was measured by a quality control-
engineer. The sample mean was ¯
x
= 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.
