Final answer:
The 95% confidence interval for the percentage of cell phone users developing brain cancer is calculated using the sample data and the standard error. If the known rate for non-users does not fall within this interval, it indicates a significant difference. A low significance level used in hypothesis testing reduces the risk of a Type I error.
Step-by-step explanation:
To calculate a 95% confidence interval for the percentage of cell phone users who develop brain or nervous system cancer, we use the sample proportion (p-hat) and the standard error of the proportion to find the margin of error. In the given example, 172 out of 420,019 cell phone users developed brain cancer, so the sample proportion (p-hat) is 172/420,019.
The standard error (SE) is calculated using the formula SE = sqrt(p-hat * (1-p-hat) / n), where n is the sample size. Once the SE is calculated, the confidence interval (CI) is p-hat ± Z*SE, where Z is the Z-score corresponding to the desired confidence level. For a 95% CI, the Z-score is typically 1.96.
To test if there's a significant difference between the rate of cancer in cell phone users versus non-users, we compare the confidence interval to the known rate for non-users. If the known rate of 0.0340% falls outside the CI, it suggests a significant difference. If the calculated CI does not contain the rate of 0.0340%, we can assert that there is evidence of a difference (Option C).
For example 9.21, since the significance level is very low (0.005), it minimizes the likelihood of a Type I error, which in turn minimizes the risk of falsely claiming that cell phone users have a higher rate of brain cancer when they actually do not.