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applied statistics and probability for engineers
Essentials Of Social Statistics For A Diverse Society 3rd Edition Anna Y Leon Guerrero, Chava Frankfort Nachmias - Solutions
For each of the variables in Exercise 3 that you classified as interval-ratio, identify whether it is discrete or continuous.
For each of the following examples, indicate whether it involves the use of descriptive or inferential statistics. Justify your answer.1./ The number of women who voted for Donald Trump in 2016 2./ Determining students’ opinion about the quality of food at the cafeteria based on a sample of 100
What level of measurement is used for the trauma variable?
Are people more likely to have experienced no traumas or only one trauma in the past year?
Explain the importance of measures of central tendency
Calculate and interpret the mode, the median, and the mean
Identify the relative strengths and weaknesses of the three measures
Determine and explain the shape of the distribution
GSS 2014 respondents were asked their opinion on whether homosexuals should have the right to marry. (The data were collected before the 2015 U.S. Supreme Court decision granting same-sex couples the right to marry.) Responses were measured on a five-point scale from strongly agree to strongly
This frequency distribution contains information on the number of hours worked last week for a sample of 32 Latino adults from the GSS 2010.
What is the level of measurement, mode, and median for “hours worked last week”?
Construct quartiles for weeks worked last year. What is the 25th percentile? The 50th percentile? The 75th percentile? Why don’t you need to calculate the 50th percentile to answer this question?
Monitoring the Future is a longitudinal study of the behaviors and attitudes of American secondary school students. Data from the 2014 survey are presented, measuring the frequency of eating breakfast (an indicator of a healthy lifestyle) by student race. The table features a different format,
U.S. households have become smaller over the years. The following table from the 2010 GSS contains information on the number of people currently aged 18 years or older living in a respondent’s household. Calculate the mean number of people living in a U.S.household in 2010.
Which category contains the 90th percentile?
We consider one more variable—2001 family income—and its relationship with students’ educational expectations. How would you describe the relationship between the two variables? Explain your answer. (Note: Some row percentages will not equal 100%due to rounding.)Source: Xianglei Chen, Joanna
We examine the relationship between highest level of parents’ education and seniors’ educational expectations. How would you characterize the relationship between the two variables?Source: Xianglei Chen, Joanna Wu, Shayna Tasoff, and Thomas Weko, Postsecondary Expectations and Plans of the High
What proportion has experienced one or more traumas in the past year?
Using the data from Exercise 1, construct appropriate graphs showing percentage distributions for race, class, and trauma.
Compute the cumulative frequency and cumulative percentage distribution for the data.
What proportion of the sample spent 3 hours or less per week on e-mail?
What proportion of the sample spent 6 or more hours per week on e-mail?
Construct a graph that best displays these data. Explain why the graph you selected is appropriate for these data.
The time-series chart shown below displays trends for presidential election voting rates by race and Hispanic origin for 1966–2012. Analysts noted how for the first time in the 2012 Presidential election black voting rates exceeded the rates for nonHispanic whites. Overall, votes cast were higher
According to the Pew Research Center (2015) recent immigrants are better educated than earlier immigrants to the United States.The change was attributed to the availability of better education in each region or country of origin. The percentage of immigrants 25 years of age and older who completed
Older Americans are often described as more politically engaged than younger Americans. One measure of political engagement is election voting. Loraine West and her U.S. Census Bureau colleagues (2014) presented the following bar graph reporting the 2012 Presidential election voting by age group.
Is there a relationship between a respondent’s country of residence and their level of agreement to the statement on immigrants?
Combining the strongly agree and agree categories, 69.1% (648 + 658/1,891) of Czechs agree that immigrants take away jobs from those born in the Czech Republic, much higher than responses from other countries. What hypothesis can you offer to explain the difference in responses?
What is the median?
Estimate the percentage of victims at the 99% confidence level. Provide an interpretation of the confidence interval.
Out of the 1,503, 56% strongly disapproved of the way President Trump was handling his job as president. Calculate the 90%confidence interval for this percentage.
From the sample, 46% of 581 Republicans and 40% of 797 Democrats said the “economic conditions in the country are excellent/good.” Calculate the 95% confidence interval for these percentages.
When asked whether economic conditions would be better a year from now, 75% of Republicans and 14% of Democrats agreed. Calculate the 99% confidence interval for both.
Throughout the 2016 Presidential election primaries, Millennials (those aged 20 to 36 years) consistently supported Senator Bernie Sanders over Secretary Hillary Clinton. According to the 2016 Gallup poll of 1,754 Millennials, 55% had a favorable opinion of Sanders than Hillary Clinton (38%).11
Calculate the 95% confidence interval to estimate the percentage of Millennials who believe that their generation has a distinctive identity as compared with the other generations (Generation X, baby boomers, or the Silent Generation).
Calculate the 99% confidence interval.
Are both these results compatible with the conclusion that the majority of Millennials believe that they have a unique identity that separates them from the previous generations?
For each reported percentage, calculate the 95% confidence interval.
Approximately 10% of GSS respondents were in the middle, some saying that homosexual relations were almost always wrong or sometimes wrong. Calculate the 95% confidence interval.
Based on your calculations, what conclusions can you draw about the public’s opinions of homosexual behavior?
Without doing any calculations, estimate the lower and upper bounds of 90% and 99% confidence intervals.
What is the 95% confidence interval for the percentage of the U.S. population who favor the death penalty for murder?
Construct the 95% confidence interval for the mean number of years of education for lower-class and working-class respondents.
Construct the 99% confidence interval for the mean number of years of education for lower-class and middle-class respondents.
As our confidence in the result increases, how does the size of the confidence interval change? Explain why this is so.
Estimate the proportion of all Canadians who believe climate change is a very serious problem at the 95% confidence interval.
Estimate the proportion of all Americans who believe climate change is a very serious problem at the 95% confidence interval.
Would you be confident in reporting that the majority (51% or higher) of Canadians and Americans believe climate change is a very serious problem? Explain.
In the GSS 2014, respondents were asked to indicate their level of agreement to the statement, “A working mother hurts children.” Of the 435 male respondents who answered the question, 18% strongly agreed that a working mother does not hurt children. Construct a 90% confidence interval for this
Of the 566 female respondents who answered the question, 40% strongly agreed that a working mother does not hurt children.Construct a 90% confidence interval for this statistic.
Why do you think there is a difference between men and women on this issue?
According to 2011 Monitoring the Future data, the average binge drinking score, for this sample of 914 teens, is 1.27, with a standard deviation of 0.80. Binge drinking is defined as the number of times the teen drank five or more alcoholic drinks during the past week. Construct the 95% confidence
Your roommate is concerned about your confidence interval calculation, arguing that severe binge drinking scores are not normally distributed, which in turn makes the confidence interval calculation meaningless. Assume your roommate is correct about the distribution of severe binge drinking scores.
Describe the assumptions of statistical hypothesis testing
Define and apply the components in hypothesis testing
Present the five-step model, testing your hypothesis at the .05 level. What do you conclude?
What is the appropriate test statistic? Why?
Test the null hypothesis with a one-tailed test (high school graduates are less likely to believe being Christian is not important at all); α = .05. What do you conclude about the difference in attitudes between high school and bachelor’s degree graduates?
If you conducted a two-tailed test with α = .05, would your decision have been different?
If you wanted to test the research hypothesis that the proportion of male voters who believe in the historical importance of the election of a woman as president is less than the proportion of female voters who believe the same, would you conduct a oneor a two-tailed test?
Test the research hypothesis at the .05 alpha level. What do you conclude?
If alpha were changed to .01, would your decision remain the same?
Interpret the group means for males and females. Which group spends more time on social media?
Assume alpha = .05 for a two-tailed test. What can you conclude about the difference in social network usage between the two groups?
If alpha were changed to .01, would your Step 5 decision change? Explain.
Is there a significant difference between married men and married women in the number of hours they have to relax during the day? Set alpha at .05.
What is the research hypothesis? Should you conduct a one- or a two-tailed test? Why?
What is your decision about the null hypothesis? What does this tell us about how representative the sample is of the American adult population?
Explain what it means to reject or fail to reject a null hypothesis
Calculate and interpret a test for two sample cases with means or proportions
Determine the significance of t-test and Z-test statistics
You are interested in finding out if the average household income of residents in your state is different from the national average household. According to the U.S. Census, for 2014, the national average household income is $53,657.15
You believe that students in small liberal arts colleges attend more parties per month than students nationwide. It is known that nationally undergraduate students attend an average of 3.2 parties per month. The average number of parties per month will be calculated from a random sample of students
A sociologist believes that the average income of elderly women is lower than the average income of elderly men.
Is there a difference in the amount of study time on-campus and off-campus students devote to their schoolwork during an average week? You prepare a survey to determine the average number of study hours for each group of students.
Reading scores for a group of third graders enrolled in an accelerated reading program are predicted to be higher than the scores for nonenrolled third graders.
Stress (measured on an ordinal scale) is predicted to be lower for adults who own dogs (or other pets) than for non–pet owners.
State the research and the null hypotheses for a two-tailed test of means.
Calculate the t statistic and test the null hypothesis at the .001 significance level. What did you find?
If alpha was changed to .01, would your Step 5 decision change? Explain.
Assuming that years of education is normally distributed in the population, what proportion of working-class respondents have 12 to 16 years of education? What proportion of upper-class respondents have 12 to 16 years of education?
What is your percentile rank?
What proportion of crime incidents had more than two victims?
What is the probability that there was more than one victim in an incident?
What proportion of crime incidents had less than four victims?
Assume that hours worked is approximately normally distributed in the sample. What is the probability that someone in the sample will work 60 hours or more in a week? How many people in the sample should have worked 60 hours or more?
What is the probability that someone will work 30 hours or fewer in a week (i.e., work part time)? How many people does this represent in the sample?
What number of hours worked per week corresponds to the 60th percentile?
Would a team be at the upper quartile (the top 25%) of the APR distribution with an APR score of 990?
What APR score should a team have to be more successful than 75% of all the teams?
What is the Z value for this score?
On which criterion (eligibility or retention) did Team A do better than Team B? Calculate appropriate statistics to answer this question.
Your score is
What percentage scored between 600 and 700 points?
What is the probability that a working-class respondent, drawn at random from the population, will have more than 16 years of education? What is the equivalent probability for a middle-class respondent drawn at random?
What is the probability that a lower-class respondent will have less than 10 years of education?
If years of education is actually positively skewed in the population, how would that change your other answers?
What percentage of students scored above 625?
What percentage of students scored between 400 and 625?
A college decides to liberalize its admission policy. As a first step, the admissions committee decides to exclude student applicants scoring below the 20th percentile on the reading SAT. Translate this percentile into a Z score. Then, calculate the equivalent SAT reading test score.
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