Suppose, Gallup asks 2100 Japanese people whether Japan will be able to completely recover from the devastation of the recent earthquake/Tsunami and and that 67% believed in the affirmative. Based on the margin of error, what should be the population percentage of Japanese who believes in the complete recovery of Japan

Question

Mathematics

Ronald Pratt

7 October, 07:56

Suppose, Gallup asks 2100 Japanese people whether Japan will be able to completely recover from the devastation of the recent earthquake/Tsunami and and that 67% believed in the affirmative. Based on the margin of error, what should be the population percentage of Japanese who believes in the complete recovery of Japan

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Answers (1)

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Herring · Answer 1

Option E) The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.

Step-by-step explanation:

Gallup asked 2100 Japanese, so the sample size is:

n = 2100

67% of the Japanese answered in affirmative. This means the proportion of population which answered in favor or affirmative is:

p = 67%

Based on his findings, Gallup constructed a confidence interval. We have to identify the correct confidence interval i. e. the population percentage of Japanese who believes in the complete recovery of Japan.

The confidence interval will always be in form of a range of values i. e. between two values: A lower limit and an upper limit. This automatically removes choices A and B from the list of correct answers.

Furthermore, the confidence interval is symmetric about the sample proportion (p), as the formula to calculate the confidence interval for a population proportion is:

(p - M. E, p + M. E)

where M. E means Margin of Error. Since, same value (M. E) is added to and subtracted from the sample proportion (p), the confidence interval will be symmetric about the sample proportion.

So, now we will find if the values in choices C, D and E are symmetric about the mean or not. If the values are symmetric the difference of the values in each option from p = 67% must be same.

Choice C)

60% and 70%

We can easily tell that these values are not symmetric about 67%. Therefore, this cannot be the answer.

Choice D)

65.13% and 70.21%

67% - 65.13% = 1.87%

70.21% - 67% = 3.21%

These two values are not symmetric either. So these cannot be our confidence interval.

Choice E)

64.82% and 69.18%

67% - 64.82% = 2.18%

69.18% - 67% = 2.18%

These two values are same distance apart from 67%, this means they are symmetric about the sample proportion. Hence, choice E is the correct confidence interval. The Margin of Error is 2.18%

The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.