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Answer:
Step-by-step explanation:
[tex]\text{The data given for the quality measurement and other criteria can be seen below:}[/tex]
Quality management Excellent Good Fair Total
Excellent 40 25 5 70
Good 35 35 10 80
Fair 25 10 15 50
Total 100 70 30 200
The null and alternative hypothesis:
[tex]\mathbf{H_o: \text{the quality management and reputation are independent} }[/tex]
[tex]\mathbf{H_a: \text{the quality management and reputation are not independent} }[/tex]
The expected value is calculated by using the formula:
[tex]E=\dfrac{row \ total \times column \ total }{table \ total}[/tex]
After using the formula to calculate the table above; we have:
The expected values of the data to be:
Quality management Excellent Good Fair Total
Excellent 35 24.5 10.5 70
Good 40 28 1.2 80
Fair 25 17.5 7.5 50
Total 100 70 30 200
Degree of freedom = ( row - 1 ) × ( column -1 )
[tex]= (3 - 1 ) \times (3 -1)[/tex]
[tex]= 2\times 2[/tex]
[tex]=4[/tex]
[tex]\text{The p-value at level of significance of 0.05 and degree of freedom of 4 = }\mathbf{0.0019}[/tex]
Decision rule: To reject the [tex]\mathbf{H_o}[/tex] if the p-value is less than the ∝
Conclusion: We reject the [tex]\mathbf{H_o}[/tex] and conclude that quality management and reputation are not independent.
(B)[tex]\text{The P-value here implies that in case that there is no dependence between the two ratings, }[/tex][tex]\text{the probability that they will seem to show at least this kind of strong dependence is 0.0019.}[/tex]
[tex]\text{Thus, the probability that they will seem to show at least this kind of strong independence is =}[/tex][tex]\mathbf{0.0019}[/tex]