Sometimes experiments involving success or failure responses are run in a paired or before/after manner. Suppose that before a major policy speech by a political candidate, n individuals are selected and asked whether (S) or not (F) they favor the candidate. Then after the speech the same n people are asked the same question. The responses can be entered in a table as follows: After S F Sx₁₂ Before FX3 X4 where x1 + x2 + x3 + x4 = n. Let P1, P2, P3, and P4 denote the four cell probabilities, so that p₁ = P(S before and S after), and so on. We wish to test the hypothesis that the true proportion of supporters (S) after the speech has not increased against the alternative that it has increased. a. State the two hypotheses of interest in terms of P1, P2, P3, and P4. b. Construct an estimator for the after/before difference in success probabilities. c. When n is large, it can be shown that the rv (X; - X;)/n has approximately a normal distribution with variance given by [P; + Pj - (P₁ - p)²]/n. Use this to construct a test statistic with approximately a standard normal distribution when Ho is true (the result is called McNemar's test). = 150, =200, and X4 x3 = d. If x₁ = 350, x₂ what do you conclude? = 300,
Sometimes experiments involving success or failure responses are run in a paired or before/after manner. Suppose that before a major policy speech by a political candidate, n individuals are selected and asked whether (S) or not (F) they favor the candidate. Then after the speech the same n people are asked the same question. The responses can be entered in a table as follows: After S F Sx₁₂ Before FX3 X4 where x1 + x2 + x3 + x4 = n. Let P1, P2, P3, and P4 denote the four cell probabilities, so that p₁ = P(S before and S after), and so on. We wish to test the hypothesis that the true proportion of supporters (S) after the speech has not increased against the alternative that it has increased. a. State the two hypotheses of interest in terms of P1, P2, P3, and P4. b. Construct an estimator for the after/before difference in success probabilities. c. When n is large, it can be shown that the rv (X; - X;)/n has approximately a normal distribution with variance given by [P; + Pj - (P₁ - p)²]/n. Use this to construct a test statistic with approximately a standard normal distribution when Ho is true (the result is called McNemar's test). = 150, =200, and X4 x3 = d. If x₁ = 350, x₂ what do you conclude? = 300,
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Question
![Sometimes experiments involving success or failure
responses are run in a paired or before/after manner.
Suppose that before a major policy speech by a political
candidate, n individuals are selected and asked whether
(S) or not (F) they favor the candidate. Then after the
speech the same n people are asked the same question.
The responses can be entered in a table as follows:
After
S F
Sx₁₂
Before
FX3 X4
where x1 + x2 + x3 + x4 = n. Let P1, P2, P3, and P4
denote the four cell probabilities, so that p₁ = P(S before
and S after), and so on. We wish to test the hypothesis that
the true proportion of supporters (S) after the speech has
not increased against the alternative that it has increased.
a. State the two hypotheses of interest in terms of P1, P2,
P3, and P4.
b. Construct an estimator for the after/before difference
in success probabilities.
c. When n is large, it can be shown that the rv (X; - X;)/n
has approximately a normal distribution with variance
given by [P; + Pj - (P₁ - p)²]/n. Use this to construct
a test statistic with approximately a standard normal
distribution when Ho is true (the result is called
McNemar's test).
= 150, =200, and X4
x3 =
d. If x₁ = 350, x₂
what do you conclude?
= 300,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe60e14a8-856f-447c-ac90-795ae43e00b4%2Fa8afab35-3055-4d9e-a00e-71f88ab743d9%2Fs2iteqb_processed.png&w=3840&q=75)
Transcribed Image Text:Sometimes experiments involving success or failure
responses are run in a paired or before/after manner.
Suppose that before a major policy speech by a political
candidate, n individuals are selected and asked whether
(S) or not (F) they favor the candidate. Then after the
speech the same n people are asked the same question.
The responses can be entered in a table as follows:
After
S F
Sx₁₂
Before
FX3 X4
where x1 + x2 + x3 + x4 = n. Let P1, P2, P3, and P4
denote the four cell probabilities, so that p₁ = P(S before
and S after), and so on. We wish to test the hypothesis that
the true proportion of supporters (S) after the speech has
not increased against the alternative that it has increased.
a. State the two hypotheses of interest in terms of P1, P2,
P3, and P4.
b. Construct an estimator for the after/before difference
in success probabilities.
c. When n is large, it can be shown that the rv (X; - X;)/n
has approximately a normal distribution with variance
given by [P; + Pj - (P₁ - p)²]/n. Use this to construct
a test statistic with approximately a standard normal
distribution when Ho is true (the result is called
McNemar's test).
= 150, =200, and X4
x3 =
d. If x₁ = 350, x₂
what do you conclude?
= 300,
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