Answer:
The 96% confidence interval for the population proportion of customers satisfied with their new computer is (0.77, 0.83).
Step-by-step explanation:
We have to calculate a 96% confidence interval for the proportion.
We consider the sample size to be the customers that responded the survey (n=800), as we can not assume the answer for the ones that did not answer.
The sample proportion is p=0.8.
[tex]p=X/n=640/800=0.8[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.8*0.2}{800}}\\\\\\ \sigma_p=\sqrt{0.0002}=0.014[/tex]
The critical z-value for a 96% confidence interval is z=2.054.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.054 \cdot 0.014=0.03[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.8-0.03=0.77\\\\UL=p+z \cdot \sigma_p = 0.8+0.03=0.83[/tex]
The 96% confidence interval for the population proportion is (0.77, 0.83).
