Unformatted text preview: 308 = 84 SOLUTION: Energizer batteries
(2)
= 100
̅ = 254 = 67
:
: −
− ≤ 45
> 45 The test statistic value:
= ( ̅ − ̅ )−( − ) = +
At (308 − 254) − 45
84
67
+
100 100 ≈ 0.8376 = 0.05, the critical value:
= = . = 1.645 Thus, at 0.05 level of significance, we cannot reject
since
< . It means that with the hypothesis testing we do not
have sufficient evidence to prove that Duracell batteries last, on average, at least 45 minutes longer than Energizer
batteries of the same size. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business  Chapter 08: The Comparison of Two Populations Example I02: (Case of the Comparison of Two Population Means by using Independent Random Samples) 13 PROBLEM I02B:
(Situation II) The power of supercomputers derives from the idea of parallel processing. Engineers at Cray Research are interested in
determining whether one of two parallel processing designs produces faster average computing time, or whether the two
designs are equally fast. The following are the results, in seconds, of independent random computation times using the
two designs.
Design 1
Design 2
2.1, 2.2, 1.9, 2.0, 1.8, 2.4,
2.6, 2.5, 2.0, 2.1, 2.6, 3.0,
2.0, 1.7, 2.3, 2.8, 1.9, 3.0,
2.3, 2.0, 2.4, 2.8, 3.1, 2.7,
2.5, 1.8, 2.2
2.6
Assume that the two populations of computing time are normally distributed and that the two population variances
are equal. Is there evidence that one parallel processing design allows for faster average computation than the other?
Design 1
(1)
= 15
̅ = 2.173 = 0.375 SOLUTION: Design 2
(2)
= 13
̅ = 2.515 = 0.351
:
: = (
( − 1) + (
− 1) + ( − 1)
− 1) = −
− =0
≠0 (15 − 1)0.375 + (13 − 1)0.351
≈ 0.1326
(15 − 1) + (13 − 1) The test statistic value:
= At = 0.05,with =( ( ̅ − ̅ )−( − 1) + ( 1 + ) −
1 = (2.515 − 2.173) − 0
1
1
0.1326 15 + 13 ≈ 2.4785 − 1) = (15 − 1) + (13 − 1) = 26, the critical value(s):
± =± ( ,) =± ( ,. ) = ±2.056 Thus, at 0.05 level of significance, we can reject
since [− , ]. It means that based on the hypothesis testing we
have sufficient evidence to prove that one parallel processing design allows for faster average computation than the
other. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business  Chapter 08: The Comparison of Two Populations International University IU 14 PROBLEM I02C:
(Situation III) Air Transport World recently named the Dutch airline KLM “Airline of the Year.” One measure of the airline’s excellent
management is its research effort in developing new routes and improving service on existing routes. The airline wanted
to test the proﬁtability of a certain transatlantic ﬂight route and offered daily ﬂights from Europe to the United States
over a period of 6 weeks on the new proposed route. Then, over a period of 9 weeks, daily ﬂights were offered from
Europe to an alternative airport in the United States. Weekly proﬁtability data for the two samples were collected, under
the assumption that these may be viewed as indepen...
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This document was uploaded on 03/01/2014 for the course ACCT 404 at Indiana State University .
 Winter '09

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