Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
9th Edition
ISBN: 9798214004020
Author: Jay L. Devore
Publisher: Cengage Learning US
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Chapter 9.1, Problem 10E
An experiment was performed to compare the fracture toughness of high-purity 18 Ni maraging steel with commercial-purity steel of the same type (Corrosion Science, 1971: 723–736). For µ = 32 specimens, the sample average toughness was
a. Assuming that σ1 = 1.2 and σ2 = 1.1, test the relevant hypotheses using α = .001.
b. Compute β for the test conducted in part (a) when μ1 − μ2 = 6.
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An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that
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tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal.
(a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁ M₂ > 0 at level 0.01.
1
Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)
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X
P-value =
State the conclusion in the problem context.
Ⓒ Reject Ho. The data suggests that the difference in average tension bond strengths exceeds 0.
O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds…
An experiment to compare the
tension bond strength of polymer
latex modified mortar (Portland
cement mortar to which polymer
latex emulsions have been added
during mixing) to that of unmodified
mortar resulted in x = 18.17 kgf/cm²
for the modified mortar (m = 42) and
y = 16.82 kgf/cm² for the unmodified
mortar (n = 31). Let μ₁ and ₂ be the
true average tension bond strengths
for the modified and unmodified
mortars, respectively. Assume that
the bond strength distributions are
both normal.
(a) Assuming that 0₁ = 1.6 and 0₂ =
1.3, test Ho: M₁ M₂ = 0 versus Ha: M₁
- H₂> 0 at level 0.01.
Calculate the test statistic and
determine the P-value. (Round your
test statistic to two decimal places
and your P-value to four decimal
places.)
Z
P-value
=
(b) Compute the probability of a type
Il error for the test of part (a) when µ₁
- H₂ = 1. (Round your answer to four
decimal places.)
(c) Suppose the investigator decided
to use a level 0.05 test and wished B
= 0.10 when M₁ M₂ = 1. If m = 42,
what…
A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The
hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for
11.5. The hardness data for a random sample of 20 tablets from one large batch are given.
the hardness is
Н
11.627
11.374
11.383
11.477
=
11.613
11.592
11.715
11.570
A hypothesis test of
Ho: μ = 11.2
Ha: μ # 11.2
11.493
11.458
11.485
11.623
11.602
11.552
11.509
11.472
11.360
11.463
11.429
11.531
where μ = the true mean hardness of the tablets using a = 0.05 has a P-value of 0.4494. Because the P-value of
0.4494 > a = = 0.05, we fail to reject Ho. We do not have convincing evidence that the true mean hardness of these tablets is
different from 11.5.
A 95% confidence interval for the true mean hardness measurement for this type of pill is (11.472, 11.561).
Which is the following statements is not true with regards to the 95% confidence…
Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
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