Question

Two different protocols for treating breast cancer were compared. One, called ALND, involves more radical surgery (more tissue is removed) with a greater risk of side effects. The other, called SLND, involves less tissue removal and possibly fewer side effects. (There is more detail about this study on p. 526 of Moore, Notz and Fligner, 6th Edition.) A group of patients is randomly assigned to one or the other treatment and the patients are followed up after five years to see if they are still disease free at that point. The results are summarized in the following table. Group Sample size Disease free after five years ALND 420 345 SLND 436 366 Do this study provide evidence significant at the 10% level that the proportions of patients who are cancer free after five years are different under the two treatments? Formulate H0 and Ha. a. Give the test statistic: b. Give the P-value: c. Your decision for the hypothesis test: A. Reject Ha. B. Reject H0. C. Do Not Reject Ha. D. Do Not Reject H0.

          Two different protocols for treating breast cancer were compared. One, called ALND, involves more radical surgery (more tissue is removed) with a greater risk of side effects. The other, called SLND, involves less tissue removal and possibly fewer side effects. (There is more detail about this study on p. 526 of Moore, Notz and Fligner, 6th Edition.)

A group of patients is randomly assigned to one or the other treatment and the patients are followed up after five years to see if they are still disease free at that point. The results are summarized in the following table.

Group Sample size Disease free after five years
ALND 420 345
SLND 436 366

Do this study provide evidence significant at the 10% level that the proportions of patients who are cancer free after five years are different under the two treatments?

Formulate H0 and Ha.

a. Give the test statistic:
b. Give the P-value:
c. Your decision for the hypothesis test:

A. Reject Ha.
B. Reject H0.
C. Do Not Reject Ha.
D. Do Not Reject H0.

Show more…

Two different protocols for treating breast cancer were compared. One, called ALND, involves more radical surgery (more tissue is removed) with a greater risk of side effects. The other, called SLND, involves less tissue removal and possibly fewer side effects. (There is more detail about this study on p. 526 of Moore, Notz and Fligner, 6th Edition.)

A group of patients is randomly assigned to one or the other treatment and the patients are followed up after five years to see if they are still disease free at that point. The results are summarized in the following table.

Group Sample size Disease free after five years
ALND 420 345
SLND 436 366

Do this study provide evidence significant at the 10% level that the proportions of patients who are cancer free after five years are different under the two treatments?

Formulate H0 and Ha.

a. Give the test statistic:
b. Give the P-value:
c. Your decision for the hypothesis test:

A. Reject Ha.
B. Reject H0.
C. Do Not Reject Ha.
D. Do Not Reject H0.

Added by Brian P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

05/11/2022

Step 1

- Alternative Hypothesis (Ha): The proportions of patients who are cancer-free after five years are different under the two treatments. ** Show more…

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Two different protocols for treating breast cancer were compared. One, called ALND, involves more radical surgery (more tissue is removed) with a greater risk of side effects. The other, called SLND, involves less tissue removal and possibly fewer side effects. (There is more detail about this study on p. 526 of Moore, Notz and Fligner, 6th Edition.) A group of patients is randomly assigned to one or the other treatment and the patients are followed up after five years to see if they are still disease free at that point. The results are summarized in the following table. Group Sample size Disease free after five years ALND 420 345 SLND 436 366 Do this study provide evidence significant at the 10% level that the proportions of patients who are cancer free after five years are different under the two treatments? Formulate H0 and Ha. a. Give the test statistic: b. Give the P-value: c. Your decision for the hypothesis test: A. Reject Ha. B. Reject H0. C. Do Not Reject Ha. D. Do Not Reject H0.

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Transcript

00:01 Hi, i'm david and i'm here to help you answer your question.

00:04 Now let me bring up your question here.

00:06 In the question here, we are going to discuss about the high -focus testing.

00:12 Here, one to test if the proportion of the patients who are cancer -free after five years are different under the two treatments.

00:24 We have the two treatments.

00:25 The first one will be the al and d.

00:27 The second one will be the sl &d.

00:29 So from each treatment we should be able to find our condition with the treatment one there will be the treatment two and therefore we want to find the sample portion phe 1 it will equal to the 345 divided by the 420 then we get equal to the 0 .82 2, 1, 4.

00:59 Similarly, for this one, we'll be able to find that b hot.

01:03 This one, this one will be 2, equal to the 366 over the 436, and then we get equal to 0 .83, 94.

01:18 So therefore, we will formulate the noon and alternative hypothesis once you find if there is a difference.

01:25 Therefore, the noon hypothesis, it will be the b hot and the hypothesis.

01:29 The p1 equal to the p2 versus the p1 will not equal to the p2 and the next time we need to find the test statistics now the formula for the test statistics i will compute down here so the test you denote to by the z the formula will be the ph1 minus the phe2 divided by the square root of the p hat 1 times 1 minus p ht 1 over and plus p .hu2 times 1 minus a ph2 over the n2 and that's going to be the formula.

02:09 So if we've looked in the value, we have the 0 .a214 minus 0 .a394 over the square root of we have the 0 .a214 times 1 minus 0 .a214.

02:28 Dividing by the n1 will be the 420.

02:31 The next one will be the 0 .8394 times 1 minus 0 .8394 over the n2 equal to the 436...

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