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

To determine if a new cancer screening method is more accurate, a hypothesis test is conducted using a four-step process starting with formulating the hypotheses and ending with making a decision based on the p-value and significance level. The method is considered more accurate if the p-value is less than 0.05.

Step-by-step explanation:

A student asks about conducting a hypothesis test to see if a new cancer screening method is more accurate than a current method which fails to detect cancer 20% of the time. Given that a sample of 200 known cancer patients were tested with the new method, and it failed to detect cancer in 30 of them, we will follow the four-step process of hypothesis testing with \( \alpha = 0.05 \).

1. Formulate the hypotheses.
2. Calculate the test statistic.
3. Determine the critical value or p-value.
4. Make a decision.

Without conducting the actual calculations, we don't have the p-value or conclusion. When full information and calculations are provided, one can complete steps 3 and 4 to draw a conclusion about the new testing method's accuracy.