1 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 - As an analyst for the Overseas Private Investment Corporation, you are required to report to Congress about guaranteed loans to companies doing business in Central American countries. You do not have time to find all the loans, so you take a sample of six loans. The loans have the following values, in millions of dollars:
3 - 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?
4. 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.
5. The Heavenly Grace Christian Elementary School has decided to examine whether using biblical materials to teach reading has an impact on reading levels. Last year, a test revealed that the average sixth-grade student read at a 5.7 grade level. This year, after all secular humanist material was deleted from the curriculum, a 20-person sample of the sixth-grade student body was tested, with the following results:
6. The Milwaukee Independent School District (MISD) is concerned with white flight-the withdrawal of white students from MISD. Last year, 63% of all MISD students were white. To get a quick reading of the situation this year, a sample of 100 students is selected: 52 of those students are white. What is your best estimate of the proportion of white students in MISD? Present a hypothesis and a null hypothesis, and evaluate them. Present a conclusion in plain English.
7. The Center for the Display of Visual Arts wants to know whether its parking situation is getting worse. Specifically, administrators are concerned that a lack of parking is driving away potential visitors. The administrators plan to address the situation if at least 15% of visitors feel that finding parking near the facility is a problem (the center averages about 3,100 visitors per week). To get a sense of whether this is really the case, the administrators distribute a brief exit survey to 150 individuals who visit the center over the following week. The results indicate that 32 of 150 visitors complained about being unable to find adequate parking. Present a hypothesis and null hypothesis. Calculate a t score and use it to evaluate the hypotheses. What should the administrators conclude from these results?