In a political campaign, one candidate has a poll taken at random from the voting population. The results of poll are that 301 out of 400 voters favor the candidate. Let P be the fraction of the voting population that favors the candidate. 0.05 (i) Test Ho: p= 0.8 against H₁ : p < 0.8 at significance level a = (ii) Test Ho: p = 0.8 against H₁ : p < 0.8 at significance level a = 0.01. (iii) Compute the associated p-value. (iv) What is the smallest significance level a for which we can reject Ho: p = 0.8 in favor of H₁ : p < 0.8?

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Exercise 3
In a political campaign, one candidate has a poll taken at random from the voting
population. The results of poll are that 301 out of 400 voters favor the candidate. Let p be
the fraction of the voting population that favors the candidate.
(i) Test Ho: p = 0.8 against H₁ p < 0.8 at significance level a = 0.05
(ii) Test Ho: p
0.8 against H₁ p < 0.8 at significance level a = 0.01.
(iii) Compute the associated p-value.
(iv) What is the smallest significance level a for which we can reject Ho: p= 0.8 in favor
of H₁ p < 0.8?
=
Transcribed Image Text:Exercise 3 In a political campaign, one candidate has a poll taken at random from the voting population. The results of poll are that 301 out of 400 voters favor the candidate. Let p be the fraction of the voting population that favors the candidate. (i) Test Ho: p = 0.8 against H₁ p < 0.8 at significance level a = 0.05 (ii) Test Ho: p 0.8 against H₁ p < 0.8 at significance level a = 0.01. (iii) Compute the associated p-value. (iv) What is the smallest significance level a for which we can reject Ho: p= 0.8 in favor of H₁ p < 0.8? =
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