Three sizes of cars are imported and sold in the Caribbean. The sizes are small,
ID: 3220154 • Letter: T
Question
Three sizes of cars are imported and sold in the Caribbean. The sizes are small, medium and large. A study was undertaken to find out whether the sales of each type of car is equally liked by the Caribbean consumers. Annual sales in hundreds of thousands for each type of car were randomly selected from six Caribbean countries. The table below shows the data for the random sample of sales:
Type of car Annual sales of cars Mean
Small
500.0
650.0
566.3
365.5
1054.6
563.3
616.6
Medium
452.3
356.6
400.0
536.6
350.0
201.1
382.8
large
600.0
402.3
650.0
365.8
675.5
1098.6
632.0
Source of Variation
Sums of Squares
Df
Mean Squares
F
Factors of Treatment
234100.2
***
***
***
Error
***
***
***
Total
917127.9
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(a) Based on the data from the table above, which type of car is the favourite choice for the average Caribbean? Justify your answer.
(b) Define the null and alternative hypothesis for the ANOVA model.
(c) What are the assumptions for the ANOVA model?
(d) Calculate the missing values for the ANOVA table above.
(e) What is your conclusion for the ANOVA results?
(f) If the means are different utilize the Tukey-Kramer procedure to determine which types of cars have different means.
Small
500.0
650.0
566.3
365.5
1054.6
563.3
616.6
Medium
452.3
356.6
400.0
536.6
350.0
201.1
382.8
large
600.0
402.3
650.0
365.8
675.5
1098.6
632.0
Explanation / Answer
a) Based on data above large size car have greater mean than medium and small size car. Large size car is the favourite choice for the average Caribbean.
b) The hypothesis are
H0 : There is no difference between the mean sales of three sizes of car.
H1 : There is difference between the mean sales of three sizes of car.
c) Assumptions :
1) Sample are independent random samples.
2) The distribution of response variable follows normal distribution.
3) Population variances are equal.
d)
e ) Fcritical = F0.05,2,15 = 3.68232
Here calculated value of F < Critical value of F
Hecne we conclude that, there is no difference between the mean sales of three sizes of car.
f) Here means are not different . Hecne there is no need to determine which types of cars have different means.
Source of Variation Sum of Squares df Mean Squares F Between Groups 234100.2 2 117050.1 2.570542 Within Groups 683027.7 15 45535.18 Total 917127.9 17Related Questions
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