Question
In: Statistics and Probability
The observed frequencies of sales of different colours of cars are shown in the following table:...
The observed frequencies of sales of different colours of cars are shown in the following table:
|
Category colour |
Black |
Red |
Green |
White |
Blue |
|
Observed Frequencies |
20 |
30 |
25 |
25 |
48 |
Calculate the chi-square test statistic to test the claim of equal probabilities.
(Round off the answer to 2 decimal digits.)
Solutions
Expert Solution
Answer:
Given that,
The observed frequencies of sales of different colours of cars are
shown in the following table:
| Category colour | Black | Red | Green | White | Blue |
| Observed Frequencies | 20 | 30 | 25 | 25 | 48 |
Calculate the chi-square test statistic to test the claim of equal probabilities:
The calculation table:
| Category Colour | Oi | Ei | (Oi-Ei)^2 | (Oi-Ei)^2/Ei |
| Black | 20 | 29.6 | 92.16 | 3.1135 |
| Red | 30 | 29.6 | 0.16 | 0.0054 |
| Green | 25 | 29.6 | 21.16 | 0.7149 |
| White | 25 | 29.6 | 21.16 | 0.7149 |
| Blue | 48 | 29.6 | 338.56 | 11.4378 |
| Total | =148 | =15.9865 |
[Under the claims equal probabilities each colour should have same frequency.]
Total frequency= 148
=148/5
=29.6
Therefore, the total frequency is 29.6.
The chi-square test statistic is,
Where,
Oi=Observed frequency
Ei= Expected frequency
=3.1135+0.0054+0.7149+0.7149+11.4378
=15.9865
=15.99 (Approximately)
Therefore, 
**Please comment on any doubt.
orchestra answered 1 year agoRelated Solutions
The observed frequencies of sales of different colours of cars are shown in the following table:...
The observed frequencies of sales of different colours of cars
are shown in the following table:
Category colour
Black
Red
Green
White
Blue
Observed Frequencies
20
30
25
25
46
Calculate the chi-square test statistic to test the claim of
equal probabilities.
The observed frequencies of sales of different colours of cars are shown in the following table:...
The observed frequencies of sales of different colours of cars
are shown in the following table:
Category colour
Black
Red
Green
White
Blue
Observed Frequencies
20
30
25
25
48
Calculate the chi-square test statistic to test the claim of
equal probabilities.
(Round off the answer to 2 decimal digits.)
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