Answer:
(0.0263%, 0.0370%)
Step-by-step explanation:
Sample size = n = 420,100
Number of users who developed cancer = x = 133
Proportion of users who developed cancer = p = [tex]\frac{133}{420100}[/tex]
Proportion of users who didnot develop cancer = q = 1 - p = [tex]1-\frac{133}{420100}=\frac{419967}{420100}[/tex]
Confidence Level = 95%
Z value associated with this confidence level = z = 1.96
The formula to calculate the confidence interval is:
[tex]\text{Lower Bound} = p-z\sqrt{\frac{pq}{n}}\\\\ \text{Upper Bound} = p+z\sqrt{\frac{pq}{n}}[/tex]
Using the values in above expressions, we get:
[tex]\text{Lower Bound}=\frac{133}{420100}-1.96\sqrt{\frac{\frac{133}{420100}\times\frac{419667}{420100}}{420100}}\\\\\text{Lower Bound}=0.000263[/tex]
and
[tex]\text{Upper Bound}=\frac{133}{420100}+1.96\sqrt{\frac{\frac{133}{420100}\times\frac{419667}{420100}}{420100}} \\\\ \text{Upper Bound}=0.000370[/tex]
Thus, the bounds of the confidence interval are:
(0.000263, 0.000370)
This can be expressed in percentages as:
(0.0263%, 0.0370%)
Therefore, a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system is (0.0263%, 0.0370%)
