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University of Maryland University

College

Stat 200 (Whealon) Quiz

3 â 80 pts

Directions:

Read & sign the academic honesty certification statement below before

taking the quiz.

The

test and work is due as specified in the âCourse Scheduleâ. Late submissions

are not accepted except in the case of extenuating documented emergencies.

This is

an open-book, open-notes quiz. A calculator, Excel or other software may be

used and are encouraged. You may add spaces as needed to show your work. You must show your

work OR cite your calculator app or website app to receive full credit. An

answer that consists of simply a number will receive no credit.

I

certify that the work submitted on and with this document represents my own

personal work. I certify that I have not collaborated with, or consulted with,

anyone else to produce the work I am submitting. I understand & agree to

abide by UMUC Policy on Academic Dishonesty and Plagiarism.

____________________________________________

Student Signature and Date

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-hatÂ± 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?