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Three professors examined awareness of four widely disseminated retirement rules among employees at the university of Utah. These rules provide simple answer to questions about retirement about retirement planning (R.N. Mayer, C.D. Zick, and M. Glattle, “public Awareness of Retirement planning Rules of Thumb,� Journal of personal Finance, 2011 10(1), 12-35). At the time of the investigation there were approximately 10,000 benefited employee and 3,095 participated in the study. Demographic data collected on these 3,095 employees included gender age (years), education level (years completed), marital status, household income ($) and employment category.
a. Describe the population of interest
b. Describe the sample that was collected.
c. Indicate whether each of the demographic variables mentioned is categorical or numerical.
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- The Capital Asset Pricing Model (CAPM) is a financial model that assumes returns on a portfolio are normally distributed. Suppose a portfolio has an average annual return of 14.7% (i.e. an average gain of 14.7%) with a standard deviation of 33%. A return of 0% means the value of the portfolio doesn't change, a negative return means that the portfolio loses money, and a positive return means that the portfolio gains money. A) What percentage of years does this portfolio lose money, i.e. have a return less than 0%? B) What is the cutoff for the highest 15% of annual returns with this portfolio?arrow_forwardIn the United States, 50% of workers classified as “private industry workers,” those working for non-government businesses, earn an hourly wage of $22.27 or more (SOURCE: National Compensation Survey: Occupational Earnings in the United States, 2010, Bulletin 2753, http://www.stats.bls.gov/ncs/ebs/). Suppose a particular family has a history of working for the government. The family has two parents and four adult-age kids. a. What is the probability that both parents and half of the kids are in the higher earning bracket of government workers? b. What is the probability that only one parent and one child fall into the higher earning bracket of government workers? c. Why is it not possible to group the entire family together as a unit of six individuals and “select two” to calculate the answer to Part b)? Calculate the answer to verify that you do not obtain the same probability by finding it this way.arrow_forwardAutoWrecks, Inc. sells auto insurance. AutoWrecks keeps close tabs on its customers' driving records, updating its rates according to the trends indicated by these records. AutoWrecks' records indicate that, ina "typical" year, roughly 70% of the company's customers do not commit a moving violation, 10% commit exactly one moving violation, 15% commit exactly two moving violations, and 5% commit three or moremoving violations.This past year's driving records for a random sample of 100 AutoWrecks customers are summarized by the first row of numbers in the table below. That row gives this year's observed frequency for each moving violation category for the sample of 100 AutoWrecks customers. The second row of numbers gives thefrequencies expected for a sample of 100 AutoWrecks customers if the moving violations distribution for this year is the same as the distribution for a "typical" year. The bottom row of numbers contains thefollowing value for each of the moving violation categories.…arrow_forward
- 10 There is some evidence that, in the years 1981 – 85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320 - 35, 1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.79%, with a standard deviation of 0.16%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years. (a) According to Chebyshev's theorem, at…arrow_forward3. 401(k) plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. Employers typically match 50% of the employee's contribution up to about 6% of salary (Fortune, Dec. 28, 1992). One company, concerned with what is believed was a low employee participation rate in its 401(k) plan, sampled 30 other companies with similar plans and asked for their 401(k) participate rates. The following rates in percentages were obtained: 80 88 90 76 85 84 81 80 82 77 79 77 82 83 75 80 75 86 85 87 60 78 60 80 79 84 82 72 70 75 Use the information to construct a 95% confidence interval for the mean participation rate for all companies that have 401(k) plans. Interpret the interval in the context of this problem.arrow_forwardFind out the next month after april income by using the forecasting method of the moving average methodarrow_forward
- Individuals filing federal income tax returns prior to March 31 had an average refund of $1102. Consider the population of “last-minute” filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15). A researcher suggests that one of the reasons that individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention. For a sample of 600 individuals who filed a return between April 10 and April 15, the sample mean refund was $1050 and the standard deviation was $500. Compute the p-value. Using α = 0.05, what is your conclusion? Test the hypotheses using the critical value approach (α = 0.025).arrow_forwardYou may need to use the appropriate appendix table or technology to answer this question. Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently averaging $100 or less per month in tax-deferred investments. A sample of 39 employees will be used to test Sparr's hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts have a population standard deviation of $75 and that a 0.05 level of significance will be used in the hypothesis test. (a) What is the type II error in this situation? O Reject Sparr Investments' claim that the employees are currently averaging $100 or less per month in tax-deferred investments when it is true. O Reject Sparr Investments' claim that the employees are currently averaging…arrow_forwardIndividuals filing federal income tax returns prior to March 31 received an average refund of $1,051. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). (a) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: μ > $1,051, Ha: μ ≤ $1,051 H0: μ = $1,051, Ha: μ ≠ $1,051 H0: μ ≥ $1,051, Ha: μ < $1,051 H0: μ ≤ $1,051, Ha: μ > $1,051 H0: μ < $1,051, Ha: μ ≥ $1,051 (b)For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of σ = $1,600 may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the…arrow_forward
- Individuals filing federal income tax returns prior to March 31 received an average refund of $1,053. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). (a) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: μ ≤ $1,053Ha: μ > $1,053H0: μ ≥ $1,053Ha: μ < $1,053 H0: μ < $1,053Ha: μ ≥ $1,053H0: μ > $1,053Ha: μ ≤ $1,053H0: μ = $1,053Ha: μ ≠ $1,053 (b) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of σ = $1,600 may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round…arrow_forwardIndividuals filing federal income tax returns prior to March 31 received an average refund of $1,064. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). (a) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention. O Ho: µ > $1,064 H3: µs $1,064 O Ho: H $1,064 O Ho: u = $1,064 H: µ + $1,064 Ο Hρ: μ > $1,064 H3: µ < $1,064 (b) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of o = $1,600 may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At a = 0.05,…arrow_forwardIndividuals filing federal income tax returns prior to March 31 received an average refund of $1,055. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15). (a) A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention. H0: ? ≤ $1,055Ha: ? > $1,055H0: ? > $1,055Ha: ? ≤ $1,055 H0: ? ≥ $1,055Ha: ? < $1,055H0: ? < $1,055Ha: ? ≥ $1,055H0: ? = $1,055Ha: ? ≠ $1,055 (b) For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of ? = $1,600 may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round…arrow_forward
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