Unformatted text preview: 5%. At
the end of the campaign, a random sample of 5,000 consumers shows that 19% of them now prefer California wines. Conduct
the test at = 0.05.
Before campaign
(1)
̂ = 0.13 = 2,060 SOLUTION: : After campaign
(2)
̂ = 0.19 = 5,000 / ℎ (1 − : −
− (1 − ≥5
)≥5 ≤ 0.05 : ≥5
)≥5 > 0.05 The test statistic value:
= At ( ̂ − ̂ )−
̂ (1 − ̂ ) = 0.05, the critical value: = + = ̂ (1 − ̂ ) . = = 1.645 ( (0.19 − 0.13) − 0.05
0.19(1 − 0.19) 0.13(1 − 0.13)
+
5,000
2,060 ≈ 1.0803 = 0.5 − 0.05 = 0.45) Thus, at 0.05 level of significance, we cannot reject
since > . It means that there is no evidence that the threemonth
campaign raised the proportion of people who prefer California wines by at least 5%. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business  Chapter 08: The Comparison of Two Populations PROBLEM 02:
(Situation II) 20 International University IU
PART III HYPOTHESIS TESTING
PROCESS Two – tailed Testing Right – tailed Testing Step 01
The populations are normally distributed
Or, the populations are assumed normal
Normal distributions
Step 02
: =
: Determine the null and
alternative
hypotheses
:
≠
:
( and )
Step 03
Compute the test statistic
value(s) ( ) and the For all instances, we always use −
critical value(s) ( ) The test statistic
value(s) ( ) The critical value(s)
() () () = = ( ( < , Powered by statisticsforbusinessiuba.blogspot.com ) ) () () = = ≤
> ( ( < , ) ) Statistics for Business  Chapter 08: The Comparison of Two Populations COMPARISON OF TWO POPULATION VARIANCES 21 International University IU
With the level of significance ( ), Situation I: We can reject
() > when Situation II: We cannot reject
() < () () () Powered by statisticsforbusinessiuba.blogspot.com > () () < () when Statistics for Business  Chapter 08: The Comparison of Two Populations Step 04
Make the decision 22 International University IU
Example III: (Case of the Comparison of Two Population Variances)
The following data are independent random samples of sales of the Nissan Pulsar model made in a joint venture of Nissan
and Alfa Romeo. The data represent sales at dealerships before and after the announcement that the Pulsar model will no
longer be made in Italy. Sales numbers are monthly.
Before: 329, 234, 423, 328, 400, 399, 326, 452, 541, 680, 456, 220
After: 212, 630, 276, 112, 872, 788, 345, 544, 110, 129, 776
Do you believe that the variance of the number of cars sold per month before the announcement is equal to the variance of
the number of cars sold per month after the announcement?
Before
(1)
= 12 = 128.03 = 16,384 SOLUTION: After
(2)
= 11 = 294.70 = 86,849.09 We assume that two populations are normally distributed
: = : ≠ The test statistic value:
() At = = 86,849.09
≈ 5.3
16,384 = 0.05, the critical value
() = ( , ) = ( , ) = 3.53 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 the variance of the number of cars sold per month before the announcement is
different from the variance of the number of cars sold per month after the announcement. Powered by statisticsforbusinessiuba.blogspot.com Statistics for Business  Chapter 08: The Comparison of Two Populations PROBLEM: 23...
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 Winter '09
 Statistics, Normal Distribution, Null hypothesis, Statistical hypothesis testing, International University IU

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