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

Category Colour
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

Total frequency = 148/5

Total frequency = 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,


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