Respuesta :
Answer:
The 98% confidence interval for the proportion of successful launches for the new rocket launching system is (0.553, 0.797).
Step-by-step explanation:
We have to calculate a 98% confidence interval for the proportion.
The sample proportion is p=0.675.
[tex]p=X/n=54/80=0.675[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.675*0.325}{80}}\\\\\\ \sigma_p=\sqrt{0.00274}=0.052[/tex]
The critical z-value for a 98% confidence interval is z=2.326.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=2.326 \cdot 0.052=0.122[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.675-0.122=0.553\\\\UL=p+z \cdot \sigma_p = 0.675+0.122=0.797[/tex]
The 98% confidence interval for the population proportion is (0.553, 0.797).
