Respuesta :
Answer:
The 95% confidence interval for the population proportion is (0.88, 0.98).
Step-by-step explanation:
We have to calculate a 95% confidence interval for the proportion.
The sample proportion is p=0.93.
[tex]p=X/n=93/100=0.93[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.93*0.07}{100}}\\\\\\ \sigma_p=\sqrt{0.00065}=0.0255[/tex]
The critical z-value for a 95% confidence interval is z=1.96.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0255=0.05[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.93-0.05=0.88\\\\UL=p+z \cdot \sigma_p = 0.93+0.05=0.98[/tex]
