Broward Community College

Math Dept.

Statistics STA2023

 Example of Test # 3

1-) You want to estimate the percentage of U.S. statistics students who get grades of B or higher. How many such students must you survey if you want 97% confidence that the sample percentage is off by no more than two percentage points?

2-) Peter and Nancy are thinking about buying the Rockwood Motel located on Interstate 70. Before they make up their minds , they want to estimate the average number of vehicles that go by the motel each day in the summer. Fortunately, the highway department has been counting vehicles on I-70 near the motel. A random sample of 36 summer days shows a sample average of 16,000 cars per day with a population standard deviation σ = 2400 cars. Find a 0.90 confidence interval for the population mean number of cars per summer day going past the Rockwood Motel.

3 -) A random sample of 5792 physicians in Colorado showed that 3139 provided at least some charity care (i.e., treated poor people at no cost). These data are based on information from State Health Care Data: Utilization, Spending, and Characteristics (American Medical Association).

(a)    Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p.

(b)   Find a 99% confidence interval for p. Give a brief explanation of the meaning of your answer in the context of this problem.

 

4-) The article "First Year Academic Success: A Prediction Combining Cognitive and Psychosocial Variables for Caucasian and African American Students"( Journal of College Student Development[1999]:599-610) reported that the sample mean and standard deviation for high school grade point average (GPA) for students enrolled at a large research university were 3.73 and 0.45, respectively. Suppose that the mean and standard deviation were based on a random sample of 900 students at the university.

    a-) Construct a 95% confidence interval for the mean high school GPA for students at this university.

    b-) Suppose that you wanted to make a statement about the range of GPAs for students at this university. Is it reasonable to say that 95% of the students at this university have GPAs in the interval you computed in Part (a) ? Explain.

5-) When consumers apply for credit, their credit is rated using FICO( Fair, Isaac, and Company) scores. Credit ratings are given below for a sample of applicants for car loans. Use the sample data to construct a 99% confidence interval for the standard deviation of FICO scores for all applicants for credit.

661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706

  

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