Question

QUESTION 4

(a) The researcher is concerned that older persons may not be knowledgeable of the COFLU-20. As such, he is interested in investigating the association between the age of the respondents and their knowledge level. Table 2 below shows the knowledge level of respondents, by age group.

Table 2

Age Group		Knowledge Level			Total
		Poor	Satisfactory	Good
	18 - 25	33	16	13	62
	26 - 34	30	18	12	60
	35 - 44	29	14	12	55
	45 - 54	36	16	18	70
	55 - 75	17	14	22	53
Total		145	78	77	300

Conduct a test, at the 5% level of significance, to determine whether the data provided sufficient evidence to conclude that an association exists between age group and knowledge level.

(i) State the hypotheses to be tested:

H₀:

H₁:                                                                                           [2 marks]

Calculate:

(ii) state the degrees of freedom for this test                                        [1 mark]

(iii) the p-value for this test, given that the chi-square test statistic, c², is 11.029.

[1 mark]

(iv) state the conclusion for the test. Give reason for your answer.     

[3 marks]

continue overleaf…/

(b) Finally, the researcher is interested in examining the regression model for knowledge, attitude and practices towards the COFLU-20. The following model was developed to forecast individual practices towards COFLU-20 using knowledge and attitude scores.

P = α + β K + δ A

where P = Practice towards COFLU-20 score

    K = Knowledge towards COFLU-20 score

    A = Attitude towards COFLU-20 score

The data are processed using MINITAB and the output in Exhibit 1 below was obtained:

Exhibit 1

The regression equation is *************

Predictor	Coef	SE	t-ratio	P
Constant	4.755	0.462	10.282	0
Knowledge	0.8	0.039	2.055	0.041
Attitude	0.024	0.6	0.393	0.695

R-sq = 81.5%

Analysis of Variance
SOURCE	DF	SS	MS	F	P
Regression	2	38.06	19.03	2.284	0.104
Error	297	2474.887	8.333
Total	299	2512.947

(i) Identify the dependent variable(s) and the independent variable(s).

   [2 marks]

(ii) Is δ significant?     

Show proof of the testing process used to arrive at your decision.      

State what this means in terms of attitude and practices.                          [4 marks]

                       

(iii) What does the value of R-sq indicate? Comment on the value of R-sq.                                                                                                                                         [2 mark]

Answer 1

i)H0:Knowledge level and age group are independent

Ha: Knowledge level and age group are not independent.

ii)dof=(5-1)*(3-1)=8

iii)pvalue=0.2

iv)As pvalue>0.05,we fail to reject H0 and say there is insufficient evidence to conclude knowledge level and age are independent.

b)i)Dependent Variable: Individual Practises

Independent Variables: Knowledge, Attitude

ii)δ is not significant. This can see from the pvalue of Attitude which is 0.695. As the pvalue>0.05, we say the coefficient of Attitude is not significant.

There is not sufficient evidence to conclude that practices can be explained by attitude

iii) R-sq indicates what percentage of the variation in the independent variables is explained by the dependent variables.

In the current model-.> Rsq=38.06/2512.95=0.015=1.5%

The current regression is a very bad model. One has to consider changing it.

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