1. Problem
The Secretary of Welfare hypothesizes that the average district office has 5% or fewer fraudulent or ineligible recipients. A sample of 10 offices reveals a mean of 4.7% with a standard deviation of 1.2%. What can be said about the secretary's hypothesis?
2. Problem
Last year, the Texas State Penitentiary averaged 14.1 violent incidents per day in its prisons. At the end of last year, the federal courts held that inmates could not supervise other inmates. Warden John Law thinks that this ruling will generate more violent incidents because, in the past, inmates used the supervision hierarchy to maintain a pecking order inside the prison. A sample of 40 days of records reveals a mean of 17.5 and a standard deviation of 2.0. What can you tell Warden Law?
3. Problem
Officials at the Special Inspector General for Afghanistan Reconstruction (SIGAR) are concerned about inventory management for parts used to repair U.S. military vehicles in the country. A comprehensive audit across all of the maintenance facilities last year revealed an average of 83 inventory errors (parts listed as available, but actually missing) per facility, per month. Officials at SIGAR want an update, but they do not have the time to do comprehensive inventory checks; accordingly, they select seven facilities for one-month reviews. Results show an average of 79 inventory errors per facility, with a standard deviation of 8.4. Can officials conclude that there has been an improvement in the inventory error rate?
4. Problem
The mayor of Chud, Wisconsin, has faced criticism over the number of water quality advisories issued last year for the city's water supply. Specifically, Chud's average water contaminant score last year was .29 (a rating of " marginally acceptable" according to the Wisconsin Department of Natural Resources). The mayor and city council took a number of aggressive steps to improve the quality of the city's water supply this year. Ideally the mayor's target for this year is an average water contaminant score of no greater than .25 (an "acceptable" rating). The mayor hires an independent consultant to analyze 80 days' worth of water samples for contaminants. What can the consultant tell the mayor after analyzing these scores? (Note: The data set for this problem is posted on Blackboard.)
5. Problem
The Metro City Rescue Mission (MCRM) depends heavily on food donations from individuals. Last year, food donations at the MCRM's curbside collection program averaged 9.1 pounds per donation. The director of MCRM would like to know whether making assumptions based on a 9.1-pound average donation is still realistic. To find out, she asks two interns to randomly select and weigh 50 unprocessed donations from the curbside collection program currently in the MCRM's warehouse. Upon analyzing the data, what should the interns tell the director? (Note: The data set for this problem is posted on Blackboard.)
6. Problem
The National TANF Recipients Organization has charged that state caseworkers are inexperienced, meaning that they have less than 3 years of experience. The Kansas State Social Welfare Department surveys its employees and finds that they have an average of 3.4 years of experience (s = 3.9, n = 200). What can the Kansas State Social Welfare Department claim?
7. Problem
The state of Michigan has just changed one of its toll roads from human collection of tolls to machine collection. The idea behind the change was to allow traffic to flow more smoothly through the toll plaza. With human attendants, the mean number of cars passing through the toll plaza was 1,253 per hour. A random sample of 100 hours under the new machine system of toll collection shows a mean of 1,261, with a standard deviation of 59. Present a hypothesis and a null hypothesis, and evaluate them. State a conclusion in plain English.
8. Problem
The director of philanthropy at the Fleckman Institute of the Arts is interested in assessing the impact that recent changes in federal tax laws have had on donations. The average donor gave $580 last year. A random sample of 50 donations reveals that in the 5 months since the laws were changed, the average donor gave $625, with a standard deviation of $97. Present a hypothesis and a null hypothesis, and evaluate them. What can the director conclude about the effect the new tax laws are having on donations?
9. Problem
The Dean of the Graduate School at Eastern Seaboard State University (ESSU) believes that graduate programs at ESSU are at a competitive disadvantage to those at peer institutions as a consequence of the relatively low teaching assistantship stipends the university offers its graduate students. The dean plans to make a case to the chancellor that additional funding for teaching assistant salaries is needed to make ESSU more competitive with its peers. The current graduate student stipend at ESSU is $11,000. To bolster her case, the dean has her assistantselect data on teaching assistantship stipends from 50 peer institutions. Based on these data, can the dean defend her position that stipends at ESSU are significantly different from those at peer institutions? (Note: The data set for this problem is posted on Blackboard.)
10. Problem
The Northeast Foundation Association (NFA) is in the process of writing an informational bulletin on the advantages of Program Related Investments, or PRIs (typically defined as loans foundations make to support programmatic goals). Officials at NFA speculate that the default rate on PRIs is at least 5%, but they want a more precise estimate for their informational bulletin. Accordingly, the chief data analyst at NFA contacts a random sample of 250 foundations in the region (that are known PRI users) and asks them to supply data on their PRI default rates. Based on the data supplied, what can NFA officials conclude? Present both null and alternative hypotheses and evaluate them. (Note: The data set for this problem is posted on Blackboard.)