Question

A study of 420,064 cell phone users found that 0.0317% 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 0.0315% for those not using cell phones. Complete parts (a) and (b).

a. Use the sample data to construct a 90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

%

(Do not round until the final answer. Then round to three decimal places as needed.)

b. Do cell phone users appear to have a rate of cancer of the brain or nervous system that is different from the rate of such cancer among those not using cell

phones? Why or why not?

4

OA. Yes, because 0.0315% is not included in the confidence interval.

OB. Yes, because 0.0315% is included in the confidence interval.

OC. No, because 0.0315% is included in the confidence interval.

OD. No, because 0.0315% is not included in the confidence interval

Answer 1

a. Step 1) From the sample, the sample percentage of cell phone users who develop the cancer is 0.0317%.

Step 2) The sample size is 420,064. Since the sample is large, we can assume the sampling distribution of sample percentages is approximately normal.

Step 3) The critical Z-value for a 90% CI is Z=1.645.

Step 4) Compute the margin of error:

MoE = Z * sqrt(p(1-p)/n) = 1.645 * sqrt(0.0317*(1-0.0317)/420,064) = 0.000330

Step 5) The 90% CI is: (0.0317 - 0.000330, 0.0317 + 0.000330) = (0.0284, 0.0350)

b. The answer is OC: No, because 0.0315% is included in the confidence interval.

Since 0.0315% falls within the confidence interval, we do not have enough evidence to conclude that the cancer rate for cell phone users is different than for non-users. The interval is reasonably wide due to the small absolute difference in percentages, so more data may be needed to detect a difference, if there is one.