Question

A method currently used to screen cancer fails to detect cancer in 20% of those who have cancer. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 200 known to have cancer were screened using the new method and it failed to detect cancer in 30. Conduct a test to see if the new method is more accurate. Use α= 0.05. Assume that the sample size is large.

Answer 1

Ans:

H₀:p=0.2

Ha:p<0.2

sample proportion=30/200=0.15

Test statistic:

z=(0.15-0.20)/sqrt(0.20*(1-0.20)/200)

z=-1.77

p-value=P(z<-1.77)=0.0384

critical z value=-1.645

As,p-value<0.05,we reject the null hypothesis.

There is sufficient evidence to conclude that new method is more accurate(i.e. fails to detect rate is lower).