STA 210 Chapter 5 Homework

Find the sample standard deviation of these 10 Presidents ages in days. You are encouraged to use a software package (suchas Microsoft Excel or STATKEY- http://www.lock5stat.com/StatKey/ (Links to an external site.) 1246.8 646.6 18854.2 19500.8

1246.8

What is the 90% confidence interval for the true average age (in days) of all U.S. Presidents, up to and including President Trump, at the time of inauguration? 18854 days to 20147 days 15036 days to 23215 days 19184 days to 21886 days 11018 days to 15963 days

18854 days to 20147 days

Inaugural Intervals A random sample of 10 U.S. Presidents was taken and the age at inauguration recorded. See Table 5.5. on page 114. Use this information for the next 5 questions. Question: What is the sample mean of these 10 Presidents' ages in days, at the time of their inauguration? You are encouraged to use a software package (such as Microsoft Excel or STATKEY- http://www.lock5stat.com/StatKey/ (Links to an external site.) HINT: Transform all ages in DAYS only 1 year=365 days 19500.8 646.6 1246.8 18854.2

19500.8

What is the correct interpretation of the 95% confidence interval (0.1, 0.4) used in the study? There is a 95% chance that the unknown parameter in this fictitious population is between 0.1 and 0.4. If many samples of size n were imagined taken from the fictitious population, and for each, a 95% confidence interval constructed, then about 95% of all those intervals would contain the true proportion of subject who would misinterpret the meaning of a confidence interval. If many samples of size n were imagined taken from the fictitious population, and for each, a 95% confidence interval constructed, then about 95% of all those intervals would contain the unknown parameter. If many samples of size 442 were imagined taken from the fictitious population, and for each, a 95% confidence interval constructed, then about 95% of all those intervals would contain the unknown parameter.

If many samples of size n were imagined taken from the fictitious population, and for each, a 95% confidence interval constructed, then about 95% of all those intervals would contain the unknown parameter.

To answer the next 4 question you may look at the graph on page 111. Also use the information bellow. 4. Sticker ShockTitle: Great Jobs, Great Lives: The 2014 Gallup-Purdue Index ReportAuthors: Gallup Organization and Purdue UniversitySource: https://www.luminafoundation.org/files/resources/galluppurdueindex-report-2014.pdf (Links to an external site.) Does it really matter where you go to college? Not so much, according to this Gallup-Purdue study. Five areas of well-being were measured among recent college graduates: purpose well-being, social well-being, financial well-being, community well-being, and physical well-being. The study concluded"that the type of schools these college graduates attended—public or private, small or large, very selective or less selective—hardly matters at all. ... Just as many graduates of public as not-for-profit private institutions are thriving -which Gallup defines as strong, consistent, and progressing"-in all areas of their well-being. " Percentages of thriving graduates among each institution type are shown in the bar chart on page 111. These results were obtained from internet surveys conducted between February 4 and March 7, 2014. The margin of error is estimated to be 1%. Question: What is the 95% confidence interval for the true thriving rates among graduates of public selective institutions? (0.09, 0.15) (0.11, 0.13) ( 0.10, 0.12) (0.15, 0.19)

( 0.10, 0.12)

What is the 95% confidence interval for the true thriving rates among graduates of private for-profit selective institutions? (0.09, 0.11) (0.03, 0.05) (0.07, 0.13) (0.01, 0.07)

(0.03, 0.05)

What is the 95% confidence interval for the true thriving rates among graduates of public non-selective institutions? (0.09, 0.11) ( 0.07, 0.13) (0.03, 0.05) (0.01, 0.07)

(0.09, 0.11)

What is the 95% confidence interval for the true thriving rates among graduates of private not-for-profit selective institutions? (0.10, 0.12) (0.09, 0.15) (0.11, 0.13) (0.15, 0.19)

(0.11, 0.13)

What is the confidence coefficient for a 90% confidence interval? 2.58 0.9 1.64 1.04

1.64

Please read below or page 106 Beyond the Numbers 1 prompt. Use this information for the next 3 questions. (You do not need to read the whole article. Information provided is enough to answer the questions. ) uthors: Robert Jones, Daniel Cox, and Juhem Navarro-RiveraSource: http://publicreligion.org/site/wp-content/uploads/2014/02/2014.LGBT_REPORT.pdf (Links to an external site.) The following is an excerpt from the Executive Summary of this report: Support for same-sex marriage jumped 21 percentage points from 2003, when Massachusetts became the first state to legalize same-sex marriage, to 2013. Currently, a majority (53%) of Americans favor allowing gay and lesbian couples to legally marry, compared to 41% who oppose. In 2003, less than one-third (32%) of Americans supported allowing gay and lesbian people to legally marry, compared to nearly 6-in-10 (59%) who opposed. Near the end of the report, the authors add: Results of the survey were based on bilingual (Spanish and English) telephone interviews conducted between November 12, 2013 and December 18, 2013, by professional interviewers under the direction of Princeton Survey Research Associates. Interviews were conducted by telephone among a random sample of 4,509 adults 18 years of age or older in the entire United States (1,801 respondents were interviewed on a cell phone, including 977 without a landline phone). The margin of error is +/- 1.7 percentage points for the general sample at the 95% confidence level. In addition to sampling error, surveys may also be subject to error or bias due to question wording, context, and order effects. Question: Using the MOE given in the article, what is the 95% confidence interval for the true proportion of Americans in favor of allowing gay and lesbian couples to marry. 30.3% to 33.7% 51.3% to 54.7% 93.3% to 96.7% 39.3% to 42.7%

51.3% to 54.7%

Using the MOE given in the article, construct a confidence interval for the true proportion of all Americans who accept the scientific evidence of global warming. 67% +/- 2.9% 67% +/- 0.29 67% +/-0.29% 0.67 +/- 2.9%

67% +/- 2.9%

In the Executive Summary, the authors state that "a majority (53%) of Americans favor allowing gay and lesbian couples to legally marry..."Were all Americans asked? How could the statement be changed so that it more precisely reflects the inference based on the sample data? No. Could say a minority of Americans sampled favor ... Yes. Could say a majority of Americans sampled favor ... Yes. Could say a majority of Americans may or may not favor ... No. Could say the sample suggests a majority of Americans favor ...

No. Could say the sample suggests a majority of Americans favor ...

Suppose you were to take another random sample of Americans at the same point in time and ask the same question. Would you find-without question-that more than 50% of the respondents were in favor of allowing gay and lesbian couples to marry? Why or why not? No. That's sampling variability. Yes. As long as each sample is a probability sample, they will yield very similar results. Yes. There it is guaranteed that the next sample statistic has to be within 1.7 percentage points of the first sample. That’s what the margin of error does for us. No. There's no way to guarantee the samples were correctly taken both times.

No. That's sampling variability.

What are the population and the parameter? Population is all Americans. The parameter is unknown but would be computed from the answers provided by those who actually answered the question. We don't know the size of the population, but the implication is that it is a population mostly of Americans. The parameter reported is that 67% accept scientific evidence of global warming. Population is all Americans. Parameter would be the true proportion of all Americans who accept scientific evidence of global warming, if it were possible to ask all Americans. We don't know the size of the population, but the implication is that it is comprised of the people working at the Pew Research Center. The parameter reported is that 67%accept scientific evidence of global warming.

Population is all Americans. Parameter would be the true proportion of all Americans who accept scientific evidence of global warming, if it were possible to ask all Americans.

What are the population and the parameter? The population is the 1,110 adults contacted by telephone, and the parameter is the 54%who say they support stricter gun laws. The population is all U.S. adults, and the parameter is the proportion of all adults who would have said they back stricter gun laws, had it been possible to ask all of them. The population is all U.S. adults, and the parameter is the 54% who said they back stricter gun laws. The population is the 1,110 adults contacted by telephone, and the parameter is the proportion of all adults who would have said they back stricter gun laws, had it been possible to ask all of them.

The population is all U.S. adults, and the parameter is the proportion of all adults who would have said they back stricter gun laws, had it been possible to ask all of them.

Use the Following Information to answer the next 3 question Americans and Their GunsTitle: Poll: Majority of Americans Back Stricter Gun LawsAuthors: Sarah Dutton, Jennifer De Pinto, Anthony Salvanto, Fred Backus and Leigh Ann Caldwell Source: CBS News January 17, 2013. http://www.cbsnews.com/8301-250_162-57564597/poll-majority-of-americans-back-stricter-gun-laws/ (Links to an external site.) As the president outlined sweeping new proposals aimed to reduce gun violence, a new CBS News/New York Times poll found that Americans back the central components of the president's proposals, including background checks, a national gun sale database, limits on high capacity magazines and a ban on semi-automatic weapons. Asked if they generally back stricter gun laws, more than half of respondents—54%—support stricter gun laws ... That is a jump from April—before the Newtown and Aurora shootings—when only 39% backed stricter gun laws but about the same as ten years ago.... This poll was conducted by telephone from January 11-15, 2013 among 1,110 adults nationwide. Phone numbers were dialed from samples of both standard land-line and cell phones. The error due to sampling for results based on the entire sample could be plus or minus three percentage points. Question: What are the sample and the statistic for the CBS News poll? The sample is all U.S. adults, and the statistic is the 54% who said they back stricter gun laws. The sample is all U.S. adults, and the statistic is the proportion of all adults who would have said they back stricter gun laws, had it been possible to ask all of them. The sample is the 1,110 adults contacted by telephone, and the statistic is the proportion of all adults who would have said they back stricter gun laws, had it been possible to ask all of them. The sample is the 1,110 adults contacted by telephone, and the statistic is the 54% who say they support stricter gun laws.

The sample is the 1,110 adults contacted by telephone, and the statistic is the 54% who say they support stricter gun laws.

A Common ChallengeA team of psychology researchers was interested in potential misinterpretations of the term "confidence" in a confidence interval. They collected data from 442 undergraduate students, 34 graduate students, and 118 of their research-active colleagues. All subjects were presented with a "fictitious scenario of a professor who conducts an experiment and reports a 95% CI for the [population proportion] that ranges from 0.1 to 0.4. Neither the topic of study nor the underlying statistical model used to compute the CI was specified in the survey." The subjects were then asked to specify whether they agreed or disagreed with each of the following statements as interpretations of that confidence interval (CI). Table 5.4 displays what the investigators found. Table is on page 112 in your textbook. Please use the information to answer the next 3 questions. All of the statements are wrong! Students and professional researchers alike found the interpretation of a confidence interval to be challenging. Yet, it is not acceptable to step away from this challenge. Confidence intervals are used everywhere as a kind of statistical seal of approval for survey and experiment results. Question: What are two things that are wrong with Statement 1? Look back in the chapter if necessary to make sure that you have the right interpretation. The statement treats the confidence interval as random, and it treats the parameter as fixed from sample to sample. The statement treats the parameter as random, and it refers nonsensically to the value of p relative to 0. The statement treats the parameter as random, and it confuses the use of 95% with that of 5%. The statement treats the parameter as random, and it treats the confidence interval as fixed from sample to sample.

The statement treats the parameter as random, and it refers nonsensically to the value of p relative to 0.

What is wrong with Statement 5? Be very clear. Look back at your content on confidence intervals to make sure that you have the right interpretation. The statement treats the confidence interval as random, and it treats the parameter as fixed from sample to sample. The statement treats the parameter as random, and it refers nonsensically to the value of p relative to 0. The statement treats the parameter as random, and it treats the confidence interval as fixed from sample to sample. The statement treats the parameter as random, and it confuses the use of 95% with that of 5%.

The statement treats the parameter as random, and it treats the confidence interval as fixed from sample to sample.

Compute an 80% confidence interval for the true proportion of Americans who "generally back stricter gun laws". What percent decrease in width is this interval from a 95% interval? The width of the interval went from 0.06 to 0.04. That is a 33.3% decrease in the interval width. The width of the interval went from 0.02 to 0.01. That is a 1.0% decrease in the interval width. The width of the interval went from 0.02 to 0.01. That is a 50% decrease in the interval width. The width of the interval went from 0.06 to 0.04. That is a 2.0% decrease in the interval width.

The width of the interval went from 0.06 to 0.04. That is a 33.3% decrease in the interval width.

Please read page 108 Beyond the numbers 2 and answer the next 3 questions using this information. Title: Americans Do Care About Climate ChangeAuthor: Annie LeonardSource: New York Times May 8, 2014. https://www.nytimes.com/roomfordebate/2014/05/08/climate-debate-isnt-so-heated-in-the-us/americans-do-care-about-climate-change . The following is an excerpt from the New York Times article: Americans do care about climate change. Polls showing lower levels of concern than in some countries don't tell the whole story. I travel widely around the U.S., attending meetings at schools, churches and community gatherings. Everywhere I go, I see people who are not only concerned about climate change, but are actively working on solutions.Nearly two-thirds (67%) of Americans accept the scientific evidence of global warming; fewer than one in six remain in denial. The full report referenced by Leonard's article tells us that the original survey was conducted by the Pew Research Center in October 2013. There was a (95%) margin of sampling error of about 2.9% associated with the entire sample. Question: What are the Pew Center poll's sample and statistic? We don't know the size of the sample, but the implication is that it is a sample of Americans. The statistic reported is that 67% accept scientific evidence of global warming. Sample is all Americans. Statistic would be those subjects who actually answered the question. Sample is all Americans. Statistic would be the true proportion of all Americans who accept scientific evidence of global warming, if it were possible to ask all Americans. We don't know the size of the population, but the implication is that it is a sample of people working at the Pew Research Center. The statistic reported is that 67% accept scientific evidence of global warming.

We don't know the size of the sample, but the implication is that it is a sample of Americans. The statistic reported is that 67% accept scientific evidence of global warming.