Solve the following questions:
1. The observed frequencies of sales of different colors of cars are shown in the following table:
|
Car Color
|
Observed Frequencies
|
|
BLACK
|
25
|
|
BLUE
|
15
|
|
GREEN
|
10
|
|
RED
|
20
|
|
WHITE
|
30
|
|
Total
|
100
|
a. A manager of a car dealership at Dammam branch claims that the probabilities of sales of different colors are equal. Write the null and alternative hypothesis and compute the expected frequencies under the null hypothesis.
b. A manager of a car dealership at Reyadh branch claims that the proportions of sales of different colors are given as Black 27%, Blue 12%, Green 11%, Red 17% and White 33%. Write the null and alternative hypothesis and compute the expected frequencies under the null hypothesis.
2. Compute the χ2 test statistic for Q.5 and test the manager's claim of equal probabilities of different colors at 5% level of significance (χ0.052 (4)=9.49).
3. Find Linear correlation coefficient between x and y
|
Hours(x)
|
1 1 3 4 6
|
|
Score (y)
|
1 3 2 5 4
|
4. Fit a regression equation between x and y for the following data:
|
Hours (x)
|
1 1 3 4 6
|
|
Score (y)
|
1 3 2 5 4
|
5. Complete the following one-way ANOVA table:
|
Source of Variation
|
SS
|
d.f.
|
MS
|
Test Statistic F
|
|
Treatment
|
162.86
|
2
|
------
|
------
|
|
Error
|
537
|
------
|
19.8
|
|
|
Total
|
------
|
29
|
|
|
6. While conducting a one-way ANOVA for comparing five treatments with 10 observations per treatment, we have the following computed values: SS(Total)= 250,SS(Error)=135,SS(Treatment)=115 and MSE = 3.
Find the value of F test statistic.