Question

4) Test the significance of variation of the retail prices of the commudity in three principle cities; Bombay, Kolkata and Delhi. The four shops were chosen at random in each city and prices observed in rupees were as follows.
Bombay 16 8 12 14
Kolkatta 14 10 10 6
Delhi 4 10 8 8

Answer 1

Answer on question 39513 – Math – Statistics

Test the significance of variation of the retail prices of the commodity in three principle cities; Bombay, Kolkata and Delhi. The four shops were chosen at random in each city and prices observed in rupees were as follows.

Bombay 16 8 12 14

Kolkata 14 10 10 6

Delhi 4 10 8 8

Do the data indicate the prices in the three cities are significantly different?

Solution

$H_0: \mu_1 = \mu_2 = \mu_{-3}$, i.e., the mean prices in the three cities are the same.

In order to simplify the calculation, subtract 10 from each observation. The deviations and their squares as follow:

$$T = \sum X_1 + \sum X_2 + \sum X_3 = 10 + 0 - 10 = 0$$ $$C.F. = \frac{T^2}{N} = \frac{0^2}{12} = 0$$

TSS=Total sum of squares $= \sum X_1^2 + \sum X_2^2 + \sum X_3^2 - C.F. = 60 + 32 + 44 - 0 = 136$

$$SSB = \left[ \frac{(\sum X_1)^2}{n_1} + \frac{(\sum X_2)^2}{n_2} + \frac{(\sum X_3)^2}{n_3} \right] - C.F. = \left[ \frac{(10)^2}{4} + \frac{(0)^2}{4} + \frac{(-10)^2}{4} \right] - 0 = 50$$

SSW=SST-SSB=136-50=86.

The various sum of squares (S.S.) along with the degrees of freedom (d.f.) are shown in the following table

For $v_1 = 2$ and $v_2 = 9$, the table value of F at 5% I.o.s. = 4*261

Since the calculated value of F is less than the table value of F the null hypothesis is accepted. We thus conclude that the mean prices in the three cities is not significantly different.