Explanation Calculation: A survey is based on the disapproval ratings of 2008 on the President of America. In the Gallup poll of 1,016 voters, 69% showed their disapproval against George W. Bush. Pundits considered the high water mark for the presidential disapproval. Previously, the disapproval rating for Nixon in 1974 was 66%. Let p be the true proportion of the George W. Bush disapproval and p ^ acts as the best estimate of p. Here, p ^ be the sample proportion and it denotes the proportion of disapproval for George W. Bush. Hypothesis: Null hypothesis: H 0 : p = 0.66 That is, the disapproval rating for George W. Bush is same as the 66% disapproval rating for Nixon. Alternative hypothesis: H A : p > 0.66 That is, the disapproval rating for George W. Bush is greater than the 66% disapproval rating of Nixon. Conditions for hypotheses test: For a given dataset, the hypotheses test for a given characteristic can be conducted reasonably, if some conditions are satisfied. Conditions: Independence assumption: The selected sample should be independent and sample should be selected at random to ensure independence. 10% condition: The size of the sample drawn should be less than 10% of the population. Success/failure condition: n p ^ ≥ 10 , n q ^ ≥ 10 Where, n be the sample size, p ^ be the sample proportion of interest and q ^ = 1 − p ^ . Requirement check: Independence assumption: The sample was taken by considering the voters as the representative of all citizens. Since it is assumed that the voters from the poll were selected at random. 10% condition: It can be assumed that the whole population is large enough so that the sample size of 1,016 is less than 10% of the population of all voters. Success/failure condition: n p ^ ≥ 10 , n q ^ ≥ 10 Substitute n as 1,016 and p ^ as 0.66, n p ^ = 1 , 016 ( 0

4th Edition

ISBN: 9780321825278

Author: Richard D. De Veaux, Paul F. Velleman, David E. Bock

Publisher: PEARSON

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Chapter R, Problem 5.29RE

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Test whether Bush’s disapproval rating is higher than Nixon’s rating.

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