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Data on 200 men and 200 women were obtained from representative | Complete Solution
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Question 1
Data on 200 men and 200 women were obtained from representative random samples of young men and women who applied for employment at a large U.S. corporation in 2012.  During the application process, each applicant was given a Reading comprehension test, a Mathematics reasoning test, along with several other exercises which were used to generate an overall competency score. A review committee used these scores along with other factors when considering the applicants for employment.  All of the applicants were between the ages of 18 and 25.  The data file is posted as exam1_employment_competency.csv attached.  You may read the file into JMP, or any other software package of your choice, to answer the following questions.  The data file contains information on the following five variables


•    Subject:  subject identification number
•    Gender:  coded 1 for females and 2 for males.
•    Reading: score on a reading comprehension test
•    Mathematics: score on a mathematics reasoning test
•    Competency:  an overall assessment of employment competency obtained from a complex combination of the scores on the reading and mathematics tests and the scores on several other tests of reasoning, communication, organization, and social skills.

 

There is one line of data for each of the 400 individuals in the sample.  To help you check if you correctly entered the data into JMP, the first five lines of the data file are shown below.

                            Subject    Gender   Reading   Mathematics   Competency
1                  1        11                20              60.4
2                  1        13                21              84.7
3                  1        11                12              44.5
4                  1          6                  4                4.0
5                  1          6                  7              11.8


Use these data to answer the following questions.

(a)    Do these data provide evidence that women perform better at Reading tasks than men? Set up appropriate null and alternate hypotheses to answer this question, report a formula and a value for your test statistic, and clearly indicate how you reached your conclusion.  Use an α = .05 significance level, and state your conclusion in the context of this study.

(b)    Construct a 99 percent confidence interval for the difference between mean Mathematics performance for women and mean Mathematics performance for men. Interpret your confidence interval in the context of the employment competence tests.  Using an α = .01 significance level, would you conclude that there is a significant difference between mean Mathematics performance for women and mean Mathematics performance for men?  Justify you answer.

(c)    Do these data provide evidence that men perform better on Mathematics related tasks than they perform on Reading related tasks?  Use a significance level of α = .05, and justify your answer.

(d)    For each of parts 1(a)–1(c) of this question, state the conditions that must be checked to validate the use of the statistical methods that you employed.  What evidence can you provide regarding whether these conditions are satisfied?

 


Question 2

The data file, student_survey.csv, consists of responses of a random sample of 60 students who earned undergraduate degrees from the social science programs at a large public university located in the southern United States.  The headings at the top of the columns refer to the following variables:
•    subject = subject identification number
•    gender = gender (female, male)
•    age = age in years
•    hsgpa= high school GPA (on a four-point scale)
•    cogpa = college GPA (on a four point scale)
•    hiv = number of people you know who have died from AIDS or who are HIV-positive
•    pa = political affiliation (D = Democrat, R = Republican, I = independent)
•    pi = political ideology (1 = very liberal, 2 = liberal, 3 = slightly liberal, 4 = moderate,
                                      5 = slightly conservative, 6 = conservative, 7 = very conservative)
•    re = how often you attend religious services (0=never, 1=occasionally, 2=most weeks,
                                                                         3=every week)
•    ab = opinion about whether abortion should be legal in the first three months of pregnancy (yes, no)
•    aa = support affirmative action (yes, no)

 

(a)    Do students tend to have higher grade point averages in college than they did in high school?  Explain how you arrived at your conclusion, and indicate what evidence you used to determine whether any necessary assumptions might be violated.

(b)    Is there evidence of a linear relationship between high school grade point average and college grade point average?  If so, it is a strong relationship?  Explain carefully how you arrived at your conclusion, making full use of available information provided by the output.  

(c)    Find the least squares estimate of the regression line for predicting college GPA from high school GPA.  Construct and interpret a 95 percent confidence interval for the slope of the population regression line for all students who have earned undergraduate degrees from the social science programs at this university

(d)    Comment on how well conditions for using a linear regression model appear to be satisfied. You may use residual plots to help with this assessment.  

(e)    Construct a 90 percent prediction interval for the undergraduate college GPA for a student with a high school GPA of 3.25.  Give an interpretation of this interval.

(f)    Is there a significant association between attitudes regarding abortion and support for affirmative action?  In your answer, be sure to clearly state the null hypothesis and the alternate hypothesis, describe how your test statistic is calculated, and check conditions for using your testing procedure.  If you cannot demonstrate that all conditions are satisfied, state your concerns but proceed with your test and report the value of the test statistic, its degrees of freedom, and the corresponding p-value.  Using a 0.05 level of significance, clearly state your conclusion in the context of the study.  If you find a significant association, describe it.
 

 

Question 3

A June 8, 2015 ABC/Washington Post Poll: “Poll Marks a Love/Hate View of the Affordable Care Act,” summarized the results of a survey of US adults on support for The Affordable Car Act. A pdf with full results, charts, and tables is available at: http://www.langerresearch.com/uploads/1169a3ACA.pdf and has been posted with this exam.

The story reads in part as:


Public support for Obamacare tied its all-time low in the latest ABC News/Washington Post poll-even as most Americans say the Supreme Court should not block federal subsidies at the heart of the health care law.
With the high court set to rule on the latest challenge to the ACA, the poll reflects the public’s split view of the law – criticism of its insurance mandate, yet support for extended coverage.
Overall, just 39 percent support the law, down 10 percentage points in a little more than a year to match the record low from three years ago as the Supreme Court debated the constitutionality of the individual mandate. A majority, 54 percent, opposes Obamacare, a scant 3 points shy of the high in late 2013 after the botched rollout of healthcare.gov.

METHODOLOGY – This ABC News/Washington Post poll was conducted by landline and cellphone telephone May 28-31, 2015, in English and Spanish, among a random national sample of 1,001 adults. Results have a margin of sampling error of 3.5 points for the full sample, including design effects. Partisan divisions are 30-22-36, Democrats-Republicans-Independents.

Additional details from the poll, including the following group breakdowns, can be found at:
http://www.washingtonpost.com/page/2010-2019/WashingtonPost/2015/06/08/National-Politics/Polling/release_398.xml

Overall, do you support the federal law that made changes to the health care system?
All 39%, Democrats 64%, Republicans 19%, Independents 35%
Overall, do you oppose the federal law that made changes to the health care system?
All 54%, Democrats 30%, Republicans 78%, Independent 56%
No Opinion
All 7%, Democrats 6%, Republicans 3%, Independent 9%


Use this information and any other information in the article to answer the following questions:

(a)    Construct 95% confidence intervals for the percent of all US adults who support the healthcare law, the percent of Democrats who support the healthcare law, Republicans who support the healthcare law, and Independents who support the healthcare law. What assumptions are necessary for these results to be valid?    

(b)    Conduct an appropriate statistical test to see whether there are any differences in the percent of the populations of Democrats, Republicans, and Independents who oppose the healthcare law.  Clearly state your null and alternative hypotheses.  Describe how the value of the test statistic is calculated, check conditions, and report the value of your test statistic, its degrees of freedom and the corresponding p-value.  Interpret your results in the context of this study.

(c)    With respect to estimating the proportion of all US adults who support the healthcare law, check to see if the reported margin of sampling error of 3.5 percentage points for all respondents is correct. Also, calculate the margin of sampling error for Democrats, Republicans, and Independents. Show all necessary calculations and explain what you conclude from these findings. In constructing your answer, feel free to use the information available at http://abcnews.go.com/PollingUnit/story?id=5984818&page=1#.UU9KJzdTk2g, which is the explanation of sampling error provided by ABC News.

(d)    ABC News is planning to do another survey in August, 2015, as part of their ongoing effort to track the current percentage of US adults who support the healthcare law.  They want to obtain an estimate with a margin of sampling error that is no larger than 1.5 percentage points.  How many adults do they need to include in their survey?   Show how you arrived at your answer.

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Data on 200 men and 200 women were obtained from representative | Complete Solution
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  • Submitted On 27 Jun, 2015 10:56:40
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Here we want to test that women perform better at Reading tasks than men thus the null and alternative hypotheses are, H_0:µ_W-µ_M≤0 and H_a:µ_W-µ_M>0 It can be seen that, this is a two sampl...
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