Question

Newly developed chemicals are usually tested to see whether they cause cancer in laboratory mice. Such an experiment can be carried out, for example, with 500 mice, of which 250 animals, selected at random, are given the chemical to be tested with their food. The remaining 250 mice serve as a control group. After a period of time, the cancer rates of both groups are compared using the two-sample t-test. The cancer rates are considered for around 25 different organs: liver, lungs, bone marrow, etc. For a particular chemical there were p-values of 0.01 for the liver, p = 0.035 for the lungs, p = 0.017 for leukemia, and 22 other p-values between 0.05 and 1. The investigators conclude that the chemical causes liver cancer. Comment on the conclusions of the examiners based on the mandatory sequence of a test.

          Newly developed chemicals are usually tested to see whether they cause cancer in
laboratory mice. Such an experiment can be carried out, for example, with 500 mice, of
which 250 animals, selected at random, are given the chemical to be tested with their
food. The remaining 250 mice serve as a control group. After a period of time, the
cancer rates of both groups are compared using the two-sample t-test. The cancer
rates are considered for around 25 different organs: liver, lungs, bone marrow, etc.
For a particular chemical there were p-values of 0.01 for the liver, p = 0.035 for the
lungs, p = 0.017 for leukemia, and 22 other p-values between 0.05 and 1. The
investigators conclude that the chemical causes liver cancer.
Comment on the conclusions of the examiners based on the mandatory sequence of a
test.

Show more…

Newly developed chemicals are usually tested to see whether they cause cancer in
laboratory mice. Such an experiment can be carried out, for example, with 500 mice, of
which 250 animals, selected at random, are given the chemical to be tested with their
food. The remaining 250 mice serve as a control group. After a period of time, the
cancer rates of both groups are compared using the two-sample t-test. The cancer
rates are considered for around 25 different organs: liver, lungs, bone marrow, etc.
For a particular chemical there were p-values of 0.01 for the liver, p = 0.035 for the
lungs, p = 0.017 for leukemia, and 22 other p-values between 0.05 and 1. The
investigators conclude that the chemical causes liver cancer.
Comment on the conclusions of the examiners based on the mandatory sequence of a
test.

Added by John L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Jon Southam

06/03/2022

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Newly developed chemicals are usually tested to see whether they cause cancer in laboratory mice. Such an experiment can be carried out, for example, with 500 mice, of which 250 animals, selected at random, are given the chemical to be tested with their food. The remaining 250 mice serve as a control group. After a period of time, the cancer rates of both groups are compared using the two-sample t-test. The cancer rates are considered for around 25 different organs: liver, lungs, bone marrow, etc. For a particular chemical there were p-values of 0.01 for the liver, p = 0.035 for the lungs, p = 0.017 for leukemia, and 22 other p-values between 0.05 and 1. The investigators conclude that the chemical causes liver cancer. Comment on the conclusions of the examiners based on the mandatory sequence of a test.

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Transcript

00:01 All righty.

00:01 So this was a fun one because you can answer this and i answered it in one way initially, but then there's another way you can do it using r which is kind of cool.

00:13 So here we're looking at the the probabilities of liver tumors under stale conditions and e.

00:21 Coli conditions in mice that are prone to tumors.

00:27 And so this is the table we're going that we have one column which is filled with mice who were in sterile conditions and whether or not they had a tumor or not.

00:37 And then the mice that had lived in non -sterile cages where there was e.

00:43 Coli present and where tumors and no tumors were recorded.

00:49 And we're looking at whether or not there's a difference in the probability of liver tumors under e.

00:55 Coli versus control conditions.

00:57 So sterile, that's your control.

00:59 A difference.

01:00 So what that means is we're looking for in terms of our hypotheses here is ps.

01:07 We're assuming that they're equal.

01:12 The alternative, what we're testing for is that ps is not equal to the pe.

01:19 So there's a difference in the proportions.

01:23 And when i first did this, i did a two sample z test.

01:27 And that's what this shows up here.

01:28 Two sample z test for proportions.

01:31 So i made a little table.

01:33 I took the data at the total.

01:35 So what he did, i got the proportions, the props here...

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