A study of 420 comma 100 cell phone users found that 133 of them developed cancer of the brain or nervous system. Prior to this study of cell phone use, the rate of such cancer was found to be 0.0449% for those not using cell phones. Complete parts (a) and (b). a. Use the sample data to construct a 95% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.
Accepted Solution
A:
Answer:(0.0263%, 0.0370%)Step-by-step explanation:Sample size = n = 420,100Number of users who developed cancer = x = 133Proportion 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 = 1.96The 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%)