Statistics 101 – Homework 9
Due Friday, December 2, 2005
Homework is due on the due date at the end of the lecture.
Reading:
November 14 – November 18
November 28 – December 2
Chapter 23
Chapters 24,25
Assignment:
1. The low temperatures (degrees Fahrenheit) for a random sample of 30 cities in the United
States are given below.
31
21
31
15
8
24
22
11
44
n = 30,
30
27
18
11
24
7
22
27
32
27
31
33
45
0
13
12
21
14
y = 23.43, s = 11.20
3
.99
.95
.90
.75
.50
.25
.10
.05
.01
2
1
0
Normal Quantile Plot
44
25
33
-1
-2
-3
10
6
4
Count
8
2
-10
0
10
20
30
40
50
Low Temperature
a) Verify that the conditions for statistical inference are met.
b) Construct a 95% confidence interval for the mean low temperature for all cities
in the United States.
c) Give an interpretation of this confidence interval.
d) Is 32o F a plausible value for the mean low temperature for all cities in the United
States? 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) 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 9
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.
90.1
94.1
91.7
92.3
91.6
93.2
91.4
92.1
92.4
a) Calculate the sample mean percentage of lean meat and the sample standard
deviation.
b) 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.
c) Based on the test in b), are the packages labeled correctly? Explain briefly.
d) One of the conditions for the test in b) is that the random sample could have
come from a population described by a normal model (the nearly normal
condition). Use the sample data to construct a box plot. Does the shape of the
box plot support the nearly normal condition? Explain briefly.
4. Data on the birth weight (grams) of 25 randomly selected male babies appear in the JMP
file MaleBirthWeight.JMP on the course web page. Use JMP to analyze the distribution
of birth weights and answer the following questions. Be sure to turn in a copy of the JMP
output with your homework.
a) Construct a 90% confidence interval for the population mean birth weight of
male babies.
b) Test the hypothesis that the population mean birth weight of male babies is 3600
grams against the alternative that the population mean birth weight is less than
3600 grams. Be sure to include all steps for the test of hypothesis.
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