Question

In: Statistics and Probability

A method currently used by doctors to screen women for possible breast cancer fails to detect...

A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 20% of the women 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 81 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in 14. Let p be the true proportion of women for which the new method fails to detect cancer. The investigator wants to conduct an appropriate test to see if the new method is more accurate using α = 0.05. Assume that the sample size is large.

Answer the following four parts

Part 1) What is the research hypothesis?

(a)Ha : p ≠ 0.20

(b)Ha : p > 0.20

(c)Ha : p < 14/81

(d)Ha : p < 0.20

Part 2) Report the value of the appropriate test statistic formula.

Part 3) What is the approximate p-value of your test?

(a)0.7291

(b)0.2291

(d)0.39

Part 4) What is the conclusion?

(a) Suﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

(b) Insuﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

Solutions

Expert Solution

Total number of sample (n) = 81

number of favourable events (X) = 14

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (0.27086668991567534)

P = 0.2709

Here, the P-value is greater than the level of significance 0.05; Fail to reject the null hypothesis

Decision Rule: Reject the null hypothesis if the test statistic value is less than the critical value -1.64 or greater than the critical value 1.64

The statistic value, -0.6111 is greater than the critical values -1.64. Therefore, we fail to reject the null hypothesis.

We have suﬃcient evidence to say that the new method is more accurate than the method currently used by the doctors

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orchestra answered 1 year ago

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