NAME:_________
You may use additional
sheets of paper to solve the following questions, but please report your
results and conclusions in the space provided.
Whenever possible, show your work for potential partial credit. NOTE:
When performing numerical calculations, keep at least 4 digits after a
decimal. (I.e., do NOT round .2265 to
.23 or .227) BUDGET YOUR TIME WISELY!
1. Every month the Bureau of Labor Statistics
conducts the Current Population Survey (CPS) and one of the outcomes of this
survey is the monthly unemployment rate.
As a researcher for the BLS your staff has contacted 60,000 households
and, through an extensive survey, have found that 5.8% of those household
members (16 years and older) surveyed fall into the BLS category of “unemployed”. In other words, the February unemployment
rate for the
a. In this situation, what are the population
parameters and point estimators? (6
points)
b. What can you say about the sampling
distribution of this point estimator?
Explain. (8 points)
2. In order to calculate the unemployment rate,
the BLS must first classify and count the total number of people in the monthly
CPS who are “unemployed”. I’ve reprinted
below an excerpt from the BLS website that describes the accuracy of the survey
results.
“A sample is not a total count and the survey may not produce the same results that would be obtained from interviewing the entire population. But the chances are 90 out of 100 that the monthly estimate of unemployment from the sample is within about 230,000 of the figure obtainable from a total census.“[1]
As
a student of quantitative methods, thoroughly explain the above excerpt
to someone who is completely unfamiliar with sampling concepts like confidence
intervals and margin of error. Be sure
to explain why the BLS feels that such a comment is necessary. (15 points)
3. A college statistics class surveys twenty-six
college sophomores and asks them how many alcoholic beverages they consume in a
typical week. The sample mean is 4.346
drinks with a standard deviation of 8.557.
a. Construct a 95% confidence interval for the
population mean of weekly drinks for college sophomores. (5 points)
b. How many students would need to be surveyed to
reduce the above margin of error by half?
Would you advise the statistics class to survey this new number of
students? Explain your reasoning. (8 points)
4. The time (in minutes) a checkout lane is idle
between customers at a supermarket follows an exponential probability
distribution with a mean of 1.2 minutes.
a. What is the probability that the next
customer will arrive between .5 and 1.0 minutes after a customer is
served? (4 points)
b. What is the probability that a checkout lane
will be idle for more than a minute between customers? (3 points)
5. According to the Bureau of Labor Statistics,
the average weekly pay for a
a. What is the probability that one worker
selected at random would earn between $490 and $590? (3 points)
b. How much does a production worker have to
earn to be in the lowest 1% of wage earners?
(4 points)
6. The research
group at the
a. Assume the research group treats the
population as an infinite population. Is
this acceptable? Explain. (4 points)
b. Assume that immediately after completing an
interview with a visitor, the interviewer returns to the entrance gate and
begins counting individuals as they enter the park. The 25th individual counted is
selected as the next person to be sampled for the survey. After completing this interview, the
interviewer returns to the entrance and again selects the 25th
individual entering the park. Does this
sampling process appear to provide a simple random sample? Explain. (6 points)
7. College administrators are noticing the
increased proportion of women enrolled in liberal arts colleges. Using a random sample of 123 college
students, researchers find that 64.23% are women. Use this sample to test the traditional assumption
that the ratio of women to men is .50.
Be sure to clearly identify the null and alternative hypotheses,
rejection range, critical value, test statistic and conclusion of the test. Finally, explain the findings to someone who
is unfamiliar with hypothesis testing.
(14 points)
8. Environmental health indicators include air
quality, water quality, and food quality.
Twenty-five years ago, 47% of
a. Declare your null and alternative hypotheses. (4 points)
b. At what level of alpha will you conduct this
test? Why did you select this
alpha? (4 points)
c. What is your critical value(s)? Show in a diagram. (2 points)
d. Compute the value of the test statistic and
p-value of this test. (4 points)
e. Thoroughly explain your conclusion to this
test. (6 points)