Question

For the test of significance questions, clearly indicate each of the formal steps in the test of significance.

Step 1: State the null and alternative hypothesis.
Step 2: Calculate the test statistic.
Step 3: Find the p-value.

Step 4: State your conclusion. (Do not just say “Reject H0” or “Do not reject H0”, state the conclusion in the context of the problem.)

A method currently used by doctors to screen patients for a certain type of cancer fails to detect cancer in 15% of the patients who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 80 patients known to this type of cancer is screened using the new method and the method failed to detect the cancer in 8 patients. At the 5% level of significance, can the researchers conclude that the new method is better than the one currently in use? (Can they conclude that the new method fails to detect cancer in less than 15% of the patients who actually have the disease?)

Answer 1

ANSWER:

1)

2)

sample proportion=8/80=0.1

Test statistic:

z=(0.1-0.15)/sqrt(0.15*(1-0.15)/80)

z=-1.252

3)

p-value=P(z<-1.252)=0.1052

4)

As,p value>0.05,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that new method is better than the one currently is use.

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