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CS DATA STRUC

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Mathematics

Date

Oct 23, 2023

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a
Probability And Statistics for Engineers And Scientists
, Hayter, A. (2007)
Math 3339
Homework 6 (Chapters 8, 10)
Name:__________________________________ PeopleSoft ID:_______________
Instructions:
•
Homework will NOT be accepted through email or in person. Homework must be submitted through
CourseWare BEFORE the deadline.
•
Print out this file and complete the problems or you can complete it using your computer.
•
Use blue or black ink or a dark pencil if completing this by hand.
•
Write your solutions in the space provided.
You must show all work for full credit.
•
Submit this assignment at
http://www.casa.uh.edu
under "
Assignments" and choose
hw6
.
•
Total possible points:
15.
1.
a
An experimenter is interested in the hypothesis testing problem with
H
0:
µ = 420
versus
H
a
:
µ ≠
420
, where μ is the average radiation level in a research laboratory. Suppose that a sample of 49
radiation level measurements is obtained and that the experimenter wishes to use
σ=10.0 for the
standard deviation of the radiation levels.
(a)
What type of hypothesis testing is this? Left-tailed? Right-tailed? Or two-tailed?
(b)
What is the rejection region when α=0.01?
(c)
Suppose that the sample mean is 415.7. What would be the experimenter's decision of the
hypothesis test based on the rejection region?
(d)
What is the p-value for this hypothesis test?

b
Devore, Jay and Berk, Kenneth,
Modern Mathematical Statistics with Applications,
Thomson Brooks/Cole, 2007.
2.
b
Water samples are taken from water used for cooling as it is being discharged from a power plant
into a river. It has been determined that as long as the mean temperature of the discharged water is at
most 15
0̊
F, there will be no negative effects on the river
'
s ecosystem. To investigate whether the
plant is in compliance with regulations that prohibit a mean discharge-water temperature above 15
0̊
,
50 water sample will be tank at randomly selected times, and the temperature of each sample will be
recorded.
(a)
Determine an appropriate null and alternative hypothesis for this test.
(b)
In the context of this situation, describe type I and type II errors.

b
Devore, Jay and Berk, Kenneth,
Modern Mathematical Statistics with Applications,
Thomson Brooks/Cole, 2007.
3.
For each of the following scenarios, state whether the null hypothesis should be rejected or not. State
any assumptions that you make beyond the information that is given.
(a)
H
0:
µ = 6
,
H
a
:
µ ≠ 6
, n=25,
x̄
=5.6, s=2.5,
α=0.05
(b)
H
0:
µ = 6
,
H
a
:
µ < 6
, n=25,
x̄
=5.6, s=2.5,
α=0.05
(c)
H
0:
µ = 25
,
H
a
:
µ > 25
, n=81,
x̄
=26.4, s=3.2,
α
=0.01
(d)
H
0:
µ = 50
,
H
a
:
µ ≠ 50
, n=55, p-value=0.053

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