Question

Suppose a mechanical engineering company is interested in patenting a new device that is intended to serve as the next generation of breast cancer screening beyond mammography. A key measurement statistic for the new device is its false positive rate. Suppose the current false positive rate for mammography is 12% with a σ of 3%, and the company tests the device on a SRS of 245 patients that results in an average false positive rate of 6.5%.

Answer 1

H0: Null Hypothesis: ( False positive rate of the new device is not less than the false positive rate of the currect device: 12%)

HA: Alternative Hypothesis: ( False positive rate of the new device is less than the false positive rate of the currect device: 12%) (Claim)

n = 245

= 0.03

= 0.065

Take = 0.05

From Table, critical value of Z = - 1.64

Test Statistic is given by:

Sincecalculated value of Z = - 28.696 is less than critical value of Z = - 1.64, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that false positive rate of the new device is less than the false positive rate of the currect device: 12%.