IE 300/GE 331 Homework 9 Solutions
1
980
Data from an Izod impact test was described in Exercise 828. The sample standard deviation was
0.25 and n=20 specimens were tested.
(a)
Test the hypothesis that
± ²³´²
against an alternative specifying that
µ ²³´²
, using
¶ ± ²³²´
, and draw a conclusion. State any necessary assumptions about underlying
distribution of the data.
(b)
What is the Pvalue for this test?
(c)
Could the question in part (a) have been answered by constructing a 99% twosided confidence
interval for
·
(a)
In order to use the
¸
·
statistic in hypothesis testing and confidence interval construction, we
need to assume that the underlying distribution is normal.
(1)
The parameter of interest is the true standard deviation of Izod impact strength,
.
However, the answer can be found by performing a hypothesis
test on
·
(2)
¹
º
»¼½
·
± ¾²³´²¿
·
(3)
¹
º
»¼½
·
µ ¾²³´²¿
·
(4)
À ± ²³²´
(5)
Á
º
·
±
¾ÂÃÄ¿Å
Æ
Ç
Æ
(6)
Reject
¹
º
if
Á
²
È
É Á
´Ê
À
È
ËÌÊ´
È
or
Á
²
È
Í Á
À
È
ËÌÊ´
È
where
Á
²³ÎÎÏË´Î
È
± Ð³ÑÒ
and
Á
²³²²ÏË´Î
È
=38.58
(7)
n=20,s=0.25,
¼Á
º
·
±
¾ÂÃÄ¿Å
Æ
Ç
Æ
±
ÄÓ¾º³·Ô¿
Æ
º³Ä
Æ
=118.75
(8)
Since 118.75>38.58, we reject
¹
º
and conclude that there is sufficient evidence to indicate
that the true standard deviation of Izod impact strength is significantly different from 0.10
at
À ± ²³²´
(b)
Pvalue<0.005
(c)
99% confidence interval for
½
·
»
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 Spring '09
 Zafarani
 Normal Distribution, Standard Deviation, Null hypothesis, Statistical hypothesis testing, true proportion

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