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University of Maryland University
College
Stat 200 (Whealon) Quiz
3 â 80 pts
Directions:
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1. (5 pts) A marketing research
company needs to estimate which of two medical plans its employees prefer. A
random sample of n employees produced the following 95% confidence interval for
the proportion of employees who prefer plan A. (0.299, 0.539) What is the point
estimate of the true proportion of
employees who prefer that plan? What is the margin of error?
2. (5 pts) A university dean is
interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean
randomly selects 200 students and finds that 118 of them are receiving
financial aid. Find a 99% confidence interval to estimate the true proportion
of students on financial aid. Express the answer in the form p-hat± E and round to the nearest
hundredth.
3. (5 pts) A simple random
sample of size n < 30 was taken. From the box plot, determine whether we should find a t-interval .jpg">
a. No, there are outliers and the
data is not normally distributed but skewed right.
b. No. Although there are no
outliers, the data is not normally distributed but is skewed right.
c. Yes, the data are normally
distributed and there are no outliers.
d. No, the data is normally
distributed but there are outliers.
4. (5 pts) From a population that
has a normal distribution, a sample of 15 randomly selected math majors has a
grade point average of 2.86 with a standard deviation of 0.78. Find the 90%
confidence interval for the population mean ?. Round to the nearest hundredth.
5. (5 pts) The principal of a
school randomly selected six students to take an aptitude test. Their scores
were:
78.2 81.3 86.1 84.2 72.8 85.2
Assume that the population has a normal distribution. Find a 90 percent
confidence interval for the mean score for all students.
6. (5 pts) A researcher at a major
clinic wishes to estimate the proportion of the adult population of the United States
that has sleep deprivation. How large a sample is needed in order to be 99%
confident that the sample proportion will not differ from the true proportion
by more than 5%?
7. (5 pts) What is meant by the
term â90% confident when constructing a confidence interval for a mean?
8. (5 pts) The reading speed of
second grade students is approximately normal with a mean of 90 words per
minute (wpm) and a standard deviation of 10 wpm. If you were to obtain 130
different simple random samples of size 25 from the population of all second
grade students and determine 90% confidence intervals for each of them, how
many of the intervals would you expect to include the reading speed of 90 wpm?
9. (5 pts) Two researchers,
Jaime and Maria, each construct confidence intervals for the proportion of a
population who is left-handed. They find the point estimate is 0.13. Each
independently constructs a confidence interval based on the point estimate.
Jaimeâs interval is (0.097, 0.163) while Mariaâs interval is (0.117, 0.173).
Which interval is wrong and why?
10. (15 pts) The following small
data set represents a simple random sample from a population whose mean is 50.
43
63
53
50
58
44
53
53
52
41
50
43
a. A normal probability plot
indicates that the data could come from a population that is normally
distributed with no outliers. Find a 95%
confidence interval for this data set.
b. Suppose the observation, 41, is
mistakenly entered as 14. Show that this observation is an outlier.
c. Find a 95% confidence interval
with the data set containing the outlier. What effect does the outlier have on
the confidence interval?
11. (20 pts) From a random
sample of 698 adult males 20 to 34 years of age, it was determined that 60 of
them have hypertension (high blood pressure).
a. Find a point estimate for the
proportion of adult males 20 to 34 years of age who have hypertension.
b. Construct a 95% confidence
interval for the proportion of adult males 20 to 34 years of age who have
hypertension.
c. You wish to conduct your own
study to determine the proportion of adult males 20 to 34 years old who have
hypertension. What sample size would be needed for the estimate to be within 3
percentage points with a 95% confidence
if you use the point estimate found in part a?
d. You wish to conduct your own
study to determine the proportion of adult males 20 to 34 years old who have
hypertension. What sample size would be needed for the estimate to be within 3
percentage points with a 95% confidence
if you donât have a prior estimate?
