Respuesta :
Answer:
Conclusion: The proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
Step-by-step explanation:
To test the claim made by the CEO of a large electric utility company the newspaper must conduct a hypothesis test for one proportion.
Assumption:
The significance level (α) of the test can be assumed to be 5%.
Hypothesis:
[tex]H_{0}:[/tex] The proportion of customers satisfied with the service they receive is 0.80, i.e. [tex]p=0.80[/tex]
[tex]H_{a}:[/tex] The proportion of customers satisfied with the service they receive is different from 0.80, i.e. [tex]p\neq 0.80[/tex]
Decision Rule:
If the p-value of the test is less than the significance level (α) then the null hypothesis may be rejected. But if the p-value is more than the significance level (α) then we cannot reject the null hypothesis.
Test Statistics:
As the sample size is large, i.e.n = 100 > 30, then according to the central limit theorem sampling distribution of sample proportion will follow the normal distribution.
The test statistic used is:
[tex]z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}} {n} }[/tex]
Given:
The p-value of the hypothesis test is computed to be 0.894.
That is:
[tex]p-value=0.894>\alpha =0.05[/tex]
This implies that we fail to reject the null hypothesis at 5% level of significance.
Conclusion:
The null hypothesis was failed to be rejected at 5% level of significance.
Thus, concluding that the proportion of customers satisfied with the service they receive from the large electric utility company is different from 80%, the claim made by the CEO.
