Question

QUESTION THREE
The administration of an inner-city college has generally assumed that the average age of a student is no more than 20 years. The standard deviation of the age of students is known to be 3.6 from previous data. However, lately the students have appeared to be older than before, and some administrators say that the average age could be higher than 20 years. You collect a random age sample of 50 students and calculate a mean of 20.76. At the 90% level of confidence, can you conclude that the average age of students has indeed increased?                                                                                                       [10 Marks]

Describe briefly two purposive sampling techniques with their uses and limitations.
                                                                                                                [5 Marks]
Football fans of both Dockers and Eagles were asked their opinion of the quality of the facilities at the Subiaco Oval. The following table cross-classifies the information provided by the fans.

Outstanding
Good
Fair
Unsatisfactory
Total

Dockers
27
35
33
25
120

Eagles
13
15
27
25
80

Total
40
50
60
50
200

At the 99% level of confidence is there a relationship between the opinion of the quality of the oval and the club the fan supports?                                                   [10 Marks]                                                                                                                                                                      

QUESTION FOUR
Give five advantages of a completely randomized design, CRD.
                                                                                                                   [5 Marks]

Suppose you are interested in developing a counselling technique to reduce stress within marriages. You randomly select two samples of married individuals out of ten churches in the association. You provide Group 1 with group counselling and study materials. You provide Group 2 with individual counselling and study materials. At the conclusion of the treatment period, you measure the level of marital stress in the group members. Here are the scores:

       Group 1                                           Group 2
: 24.13                                        22.88
: 5.64                            6.14

Are these groups significantly different in marital stress? Test at 5% level of significance.
                                                                                                                     [10 Marks]
A manufacturer claims that the average weight of a tin of baked beans is 440 g and the standard deviation is known to be 20 g. From a random sample of 100 cans you calculate the average weight to be 435 g. At the 95% level of confidence, is there a change in the average weight of a can of baked beans?                                                 [10 Marks]

QUESTION FIVE
A machine which fills orange squash bottles should be set to deliver 725 ml. A sample of 50 bottles is checked and the mean quantity is found to be 721 ml and the sample s.d. is 13 ml. Does this differ significantly from 725 ml at the 1% level? Find the probability of Type I error for this test.                                                                               [10 Marks]

Prove the formula.                                           [5 Marks]

A random sample of 10 hot drinks from Dispenser A had a mean volume of 203ml and a standard deviation of 3ml. A random sample of 15 hot drinks from Dispenser B gave corresponding values of 206ml and 5ml. The amount dispensed by each machine maybe assumed to be normally distributed. Test at the 5% significance level, the hypothesis that there is no difference in the variability of the volume dispensed by the two machines.

                                                                                                                 [10 Marks]
QUESTION SIX
A scientist, working in an agricultural research station, believes there is a relationship between the hardness of the shell of eggs laid by chickens and the amount of a certain food supplement put into the diet of the chickens. He selects ten chickens of the same breed and collects the data given below:
Chicken
A
B
C
D
E
F
G
H
I
J

Food supp x(g)
7.0
9.8
11.6
17.5
7.6
8.2
12.4
17.5
9.5
19.5

Hardness of shells y
1.2
2.1
3.4
6.1
1.3
1.7
3.4
6.2
2.1
7.1

Calculate the equation of the regression line of y on x

Calculate the correlation coefficient, (r).

Calculate the coefficient of determination and interpret its meaning

                    

Answer 1

6)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	120.60	34.60	186.92	44.30	90.77
mean	12.06	3.46	SSxx	SSyy	SSxy

a)

sample size ,   n =   10          
here, x̅ = Σx / n=   12.060   ,     ȳ = Σy/n =   3.460  
               0.286898839  
SSxx =    Σ(x-x̅)² =    186.9240          
SSxy=   Σ(x-x̅)(y-ȳ) =   90.8          
                  
estimated slope , ß1 = SSxy/SSxx =   90.8   /   186.924   =   0.48562
                  
intercept,   ß0 = y̅-ß1* x̄ =   -2.39658          
                  
so, regression line is Ŷ =   -2.3966   +   0.4856   *x

b) correlation coefficient ,    r = SSxy/√(SSx.SSy) =   0.9975

c) R² =    (SSxy)²/(SSx.SSy) =    0.9950

Approx 99.50% of variation in variable y is explained by variable X