Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 8, Problem 59SE
It is specified that a certain type of iron should contain .85 g of silicon per 100 g of iron (.85%). The silicon content of each of 25 randomly selected iron specimens was determined, and the accompanying Minitab output resulted from a test of the appropriate hypotheses.
| Variable | N | Mean | StDev | SE Mean | T | P |
| sil cont | 25 | 0.8880 | 0.1807 | 0.0361 | 1.05 | 0.30 |
- a. What hypotheses were tested?
- b. What conclusion would be reached for a significance level of .05, and why? Answer the same question for a significance level of .10.
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A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: 104.3 89.6 89.9 95.6 95.2 90.0 98.8 103.7 98.3 106.4 102.0 91.1
a)Does this data suggest that the population mean reading under these conditions differs from 100? State and test the appropriate hypotheses using =.05.
b) Suppose that prior to the experiment, a value of teta=7.5 had been assumed. How many determinations would then have been appropriate to obtain beta=.10 for the alternative u=95 ?
A sample of 12 radon detectors of a certain type was selected, and each was exposed to
100 pCi/L of radon. The resulting readings were as follows:
105.6
90.9
91.2
96.9
96.5
91.3
100.1
105.5
99.6
107.7
103.3
92.4
Does this data suggest that the population mean reading under these conditions differ
from 100?
(a)
State the null and alternative hypotheses.
(b)
Calculate, correct to 2 decimal places,
(i)
the sample mean, x ; and
(ii)
the sample standard deviation, s.
(c)
Evaluate the appropriate test statistic.
(d)
Test these hypotheses at 0.05 level of significance.
An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberry drink and another sample filled with cola.
Beverage
Sample Size
Sample Mean
Sample SD
Strawberry Drink
10
535
24
Cola
10
559
15
Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use
? = 0.05.)
State the relevant hypotheses. (Use ?1 for the strawberry drink and ?2 for the cola.)
H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≥ 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 ≠ 0 H0: ?1 − ?2 = 0Ha: ?1 − ?2 < 0H0: ?1 − ?2 = 0Ha: ?1 − ?2 > 0
Calculate the test statistic and determine the P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t
=
P-value
=
State the conclusion in the problem context.
Reject H0. The data suggests that cola has a higher average compression strength than the strawberry drink.Reject H0. The…
Chapter 8 Solutions
Probability and Statistics for Engineering and the Sciences
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