BA 301 Chapter 8 Homework
In this chapter, you learned about 5 types of confidence intervals. They are:
- Confidence interval for a mean
- Confidence interval for a proportion
- Confidence interval for the difference between means – independent samples
- Confidence interval for the difference between means – paired samples
- Confidence interval for the difference between proportions
Q1) Sheet Q1 Data contains fictional data on a number of business students who graduated in 2010 from two universities. The variables are:
- Student: an identifier variable,
- University: State University or Killingsworth College,
- Gender: Male or Female,
- Major: the business major concentration: Marketing/Management, Accounting/Finance, and Other Business (e.g. human resources, operations management, or business economics,)
- Salary 2010: the graduate’s starting salary,
- Salary 2012: the graduate’s salary two years later, and
- GPA: the graduate’s final GPA.
For each question below, identify which of the 5 types of confidence intervals should be calculated, the confidence level, and the variable(s) involved. Do not actually perform the calculations.
- a) Form a 95% confidence interval for the average GPA of a Killingsworth graduate.
- b) Do male and female business students have different starting salaries (2010) on average? Form a 99% confidence interval to examine this question.
- c) Determine a 95% confidence interval for the proportion of students who are Acct/Fin majors.
- d) Is there a difference between the proportion of men who major in Mktg/Mgmt as opposed to the proportion of women who major in Mktg/Mgmt? Use a 90% confidence level to estimate the difference.
- e) Estimate, with 95% confidence, the average increase in salary these business graduates have received from 2010 to 2012.
Q2) Sheet Q2 Data contains information from a sample of 178 students accepted to Harrigan University. The variables are:
- Applicant: An identifier variable,
- Accepted: whether the applicant accepts Harrigan’s offer to enroll,
- MainRival: whether the applicant enrolls at Harrigan’s main rival university,
- HSClubs: number of high school clubs applicant served as an officer,
- HSSports: number of varsity letters applicant earned,
- HSPGA: applicant’s high school GPA,
- HSPctile: applicant’s percentile (in terms of GPA) in his or her graduating class,
- HSSize: number of students in applicant’s graduating class,
- SAT: applicant’s combined SAT score,
- CombinedScore: a combined score for the applicant used by Harrigan to rank applicants.
Answer the following questions. There is no need to interpret your calculations – just do them.
- What proportion of those who were offered admission to Harrigan enrolled there? Form a 99% confidence interval to estimate this proportion. The variable to analyze is Accepted.
- What is the average number of high school varsity letters that a student accepted at Harrigan receives? Estimate this confidence interval for a mean using a 90% confidence level. The variable you are to analyze is HSSports.
- Estimate the difference between the average combined score received by a student who elects to enroll at Harrigan and one who does not. Use a 95% confidence interval for the difference between means – independent samples. The variables to be analyzed are CombinedScore and Accepted=Yes and No.
- Of students who received a scholarship offer, is there a difference in the proportion of students who enroll at Harrigan and those who do not? Use a 90% confidence level to assess this confidence interval for the difference between proportions. The variables to be analyzed are Scholarship=Yes and Accepted=Yes and No.
Q3) Sheet Q3 Data contains information for publicly traded companies (and we have used this data before.) The variables are:
- Company Name: the name of the company,
- Company Type: the industry in which the company primarily competes,
- Executive Name: the name of the CEO,
- Salary 2008: base salary earned in 2008,
- Bonus 2008: whether a bonus was paid to the CEO in 2008,
- Comp 2008: total compensation of salary and bonus paid to the CEO in 2008,
- Salary 2003: base salary earned in 2003,
- Bonus 2003: whether a bonus was paid to the CEO in 2003,
- Comp 2003: total compensation of salary and bonus paid to the CEO in 2003, and
- Same CEO?: whether the executive for 2008 was also the CEO in 2003.
Please note that the 2003 variables have some data points missing. This is because data was not collected for those companies in 2003. In general, you should not be worried about this – the net effect is that for some questions the sample sizes will be reduced.
Given the analysis for each question, interpret the outputs. Be sure to state the results of the confidence interval (“we are X% confident that the true population parameter is between X and X”) and whether that meets the criteria given.
- A lot of attention has recently been focused on CEO compensation. Given the confidence interval in sheet Q3a, can we say that on average CEOs earned more than $2.75 million in 2008?
- With the aging of the baby boomers, one growth industry that is expected to continue growing is health care. The confidence interval in sheet Q3b shows the proportion of companies that are engaged in health care as of 2008. It is expected that at least 10% of companies should be involved in health care in the coming years. Was that goal reached in 2008?
- I wonder if executives in some industries tend to get paid more than those in other industries. Given the confidence interval in sheet Q3c, can we say that CEOs in telecommunications companies made more than those in utilities companies in 2008?
- The position of CEO can be a perilous one, especially in tough economic times. For the group surveyed, were more than half the CEOs employed by the same company in 2003 and 2008 for long terms of employment? Use the confidence interval shown in sheet Q3d to answer the question.
- Observe the confidence interval shown in sheet Q3e. For the CEOs who were employed by the same company in 2003 and 2008, did their total compensation drop in that time period?
Q4) Sheet Q4 Data shows a confidence interval that shows the results of a recent political poll. A random sample of voters was asked for which candidate they were likely to vote in an upcoming election. XYZ news reported the following:
“George Gonzales is leading in the polls, followed by Eddie English.”
Is this statement correct, and is it reasonable to say that Gonzales is leading English?