**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 |

** **