Answered: 1. Using the information given above,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

America’s image abroad ~ Around the world, favorable views of the U.S. rebounded in 2021, according to an article published by the Pew Research Center in June 2021. Between March 12 and May 26, 2021, Pew Research contacted a nationally representative sample of adults in 16 different countries around the world. One of the questions in the survey asked participants whether they have a favorable view of the U.S.

Of the 1022 respondents who participated in the survey in Germany, 613 said that their view of the U.S. is favorable. (Values given in this problem are consistent with the results reported in the article.)

Assume the respondents are a simple random sample of all adults in Germany. Round all calculated answers to 4 decimal places unless otherwise indicated.

1. Using the information given above, construct a 90% confidence interval for the true proportion of adults in Germany who have a favorable view of the U.S.

( , )

2. Which of the following conditions must be met for the confidence interval to be valid? Select all that apply.

A. The observations must be independent of one another.

B. There must be at least 10 'success' and 10 'failure' observations in the sample.

C. The sample proportion must be normally distributed.

D. The value for p must be less than 0.10 to provide evidence against the null hypothesis.

3. The information from the sample described above estimates the standard error to be ???̂=SEp^= 0.0153. Which of the statements below is a correct interpretation of this standard error?

A. On average, for repeated simple random samples of this size, we expect the sample proportion to be approximately 0.0153 from the true population proportion of adults in Germany with a favorable view of the U.S.
B. We have strong evidence that the true proportion of adults in Germany with a favorable view of the U.S. is contained in the confidence interval constructed with this sample information.
C. There is a 1.53% chance that the sample proportion is contained within any confidence interval for the true proportion of adults in Germany with a favorable view of the U.S.
D. The sample proportion is different from the true proportion of adults in Germany with a favorable view of the U.S. approximately 1.53% of the time.

4. Pew Research also surveyed a random sample of 1563 adults living in Australia. Using the sample information reported in the article, we calculate a 95% confidence interval for the true proportion of adults in Australia with a favorable view of the U.S. to be (0.455, 0.596).

Which of the following statements are appropriate interpretations in this scenario? Select all that apply.

A. We can be 95% confident that, on average, the margin of error will vary no more than the size of the standard error.

B. We can be 95% confident that the true proportion of adults in Australia with a favorable view of the U.S. is contained in the interval (0.455, 0.596).

C. If the researchers collected 100 samples of size n = 1563 from this population and constructed a 95% confidence interval for each of the 100 samples, they could expect approximately 95 of them to contain the true proportion of adults in Australia with a favorable view of the U.S.

D. On average, 95% of the time we can expect any sample proportion from a sample of 1563 adults in Australia with a favorable view of the U.S. to be in the interval (0.455, 0.596).

5. If, instead, we used the results for Australia to calculate a 99% confidence interval for the true proportion of adults in Australia with a favorable view of the U.S., this new interval would be the 95% confidence interval.

6. For this article, Pew Research surveyed adults in 16 different countries. Overall, 61% of survey respondents said their view of the U.S. was favorable. Peru was not one of the these 16 countries. If a research group in Peru wanted to construct a 90% confidence interval for the proportion of adults in that country who have a favorable view of the U.S. with a margin of error of no more than 4%, what size sample should they take?

Use the overall value from the Pew Research survey as a planning value for ?∗p∗, that is, ?∗=0.61p∗=0.61. Round your ?∗z∗ value to exactly 3 decimal places. Your answer should be an integer.

?=n=

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