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In an analysis of variance problem involving 3 treatments and 10 observations per treatment, SSE = 399.6. The MSE for this situation is
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support
capital punishment?
|
Number of
individuals
|
Yes
|
40
|
No
|
60
|
No Opinion
|
50
|
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
In th e last presidential election, before the candidates started their major campaigns, the percentages of registered voters who favored the various candidates were as follows.
|
|
Percentages
|
|
Republicans
|
34%
|
|
Democrats
|
43%
|
|
Independents
|
23%
|
After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. We are interested in determining whether the proportion of voters who favored the various candidates had changed.
Compute the test statistic (c2).
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen
|
83
|
Sophomores
|
68
|
Juniors
|
85
|
Seniors
|
64
|
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
The expected frequency of seniors is
Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With = 0.05, test to see if the methods of payment have changed during the Christmas rush. CALCULATE
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support
capital punishment?
|
Number of
individuals
|
Yes
|
40
|
No
|
60
|
No Opinion
|
50
|
We are interested in determining whether or not the opinions of the individuals (as to Yes, No, and No Opinion) are uniformly distributed.
The calculated value for
the test statistic equals
In the ANOVA, treatment refers to
ANOVA
|
|
|
|
|
|
|
Source of Variation
|
SS
|
df
|
MS
|
F
|
P-value
|
F critical
|
Between Groups
|
70
|
2
|
|
"A"
|
|
|
Within Groups
|
62
|
12
|
|
|
|
|
Total
|
132
|
14
|
|
|
|
|
Th w what is calculate "A".
From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. We are interested in determining if the selection of a TV station is independent of the level of education.
| Educational Level | |||
| High School | Bachelor | Graduate | TOTAL |
|
|
|
|
|
Public Broadcasting | 50 | 150 | 80 | 280 |
Commercial Stations | 150 | 250 | 120 | 520 |
|
|
|
|
|
TOTAL | 200 | 400 | 200 | 800 |
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
Freshmen
|
83
|
Sophomores
|
68
|
Juniors
|
85
|
Seniors
|
64
|
We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.
The expected number of
freshmen is
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