Statistics 101 – Homework 9
Due Friday, April 20, 2007
Homework is due on the due date at the end of the lecture.
Reading:
April 9 – April 13
April 16 – April 20
Chapter 23
Chapters 24,25
Assignment:
1. In a study of youths in the East Boston area, several different measurements were made
on girls age 5 to 17. Below are the heights (inches) of 24 randomly selected girls from
East Boston.
60.0
63.0
52.0
64.5
59.0
62.0
64.0
62.0
54.0
71.0
61.5
64.5
56.5
63.5
62.5
68.0
64.5
65.0
59.0
60.0
57.5
67.5
68.0
70.0
3
.99
.95
.90
.75
.50
.25
.10
.05
.01
2
1
0
Normal Quantile Plot
n = 24 , y = 62.48, s = 4.74
-1
-2
-3
12
8
6
Count
10
4
2
50
55
60
65
70
75
Height
a) Verify that the nearly normal condition for statistical inference is met.
b) Construct a 95% confidence interval for the mean height of all girls in East
Boston age 5 to 17.
c) Give an interpretation of this confidence interval.
d) Is 60 inches a plausible value for the mean height of girls age 5 to 17 in East
Boston? Support your answer by referring to the confidence interval you
constructed in b).
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2. Go to the following web site
http://statweb.calpoly.edu/chance/applets/ConfSim/ConfSim.html
For the method select Means. When you do this, a second box will appear with “z with
sigma” in it. Go to the pull down for that box and select “t”.
a) In the box labeled n, enter 10. In the box labeled intervals, enter 250. Click on
Sample. Of the 250 intervals constructed how many contain the population
mean, µ?
b) In the box labeled conf level, change 95 to 90 and click on Recalculate. What do
you notice about the width of the intervals now compared to those in a)? How
many of the intervals contain the population mean, µ?
c) In the box labeled conf level, change 90 to 98 and click on Recalculate. What do
you notice about the width of the intervals now compared to those in b)? How
many of the intervals contain the population mean, µ?
d) What effect does changing the level of confidence have on the width of
confidence intervals?
e) Reset the simulation and enter 95 in the conf level box. Click on Sample. Now
change the sample size from 10 to 100 in the box labeled n and click on Sample
again. Describe the effect that changing the sample size from 10 to 100 has on
the width of the confidence intervals.
f) Reset the simulation and enter 95 in the conf level box. Click the Sample button
enough times so that the running total is out of 5000. Report the value of the
running total as a fraction and as a %. What should the long run running total
be?
3. The local grocery store packages different grades (based on fat content) of hamburger.
Usually the leaner (less fat) grades are more expensive. A simple random sample of 12
one-pound packages of hamburger is obtained from the local store and tested for fat
content. Below are the percentages of lean meat for each package.
90.9
94.3
91.9
92.5
91.8 93.4
91.6
92.6
92.3
93.6
93.1
93.2
a) Calculate the sample mean percentage of lean meat and the sample standard
deviation.
b) Use the sample data to construct a box plot. Does the shape of the box plot
support the nearly normal condition? Explain briefly.
c) The packages are labeled 93% lean. Use the summaries in a) to test the
hypothesis H0: µ = 93 against HA: µ < 93, where µ is the population mean
percentage lean. Be sure to calculate the appropriate test statistic and P-value,
reach a decision and justify that decision, and state a conclusion.
d) Based on the test in b), are the packages labeled correctly? Explain briefly.
4. Earlier in the semester on homework #1 data on body temperature were given. A JMP
file on the course web page (BodyTemp_Females.JMP) contains data on the body
temperature (oF) for 65 randomly selected females. Turn in the JMP output with your
answer to the following.
a) Construct a 90% confidence interval for the population mean body temperature
for females.
b) Test the hypothesis that the population mean body temperatures for females is
98.6 oF against the alternative that the population mean body temperatures for
females is less than 98.6 oF. Be sure to include all steps for the test of
hypothesis.
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