Answer to Question #179098 in Statistics and Probability for Mala Kumari

Question

) To test the significance of variation in the retail prices of a commodity in three principle cities, 

Mumbai, Kolkata and Delhi, four shops were chosen at random in each city and the prices who lack 

confidence in their mathematical ability observed in rupees were as follows:

MUMBAI: 16 8 12 14

KOLKATA: 14 10 10 6

Delhi : 4 10 8 8

Do the data indicate that the price in the three cities are significant different? (7 marks)

Answer 1

$H_0:\ \mu_1=\mu_2=\mu_3$

In order to simplify the calculation, subtract 10 from each observation. Then:

$T=\sum X_1+\sum X_2+\sum X_3=10+0-10=0$

$C.F.=T^2/N=0$

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

$SSB=\frac{(\sum X_1)^2}{n_1}+\frac{(\sum X_2)^2}{n_2}+\frac{(\sum X_3)^2}{n_3}-C.F.=50$

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

For source of variation (between city):

Sum of square$=50$ ; Degrees of freedom$=3-1=2$

Mean sum of squares$=25$

For source of variation (within city):

Sum of square$=86$ ; Degrees of freedom$=2$

Mean sum of squares$=9.556$

Then: $F=25/9.556=2.616$

For $df_1=2,df_2=9$:

the table value of $F$ at 5%: $F=4.261$

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.