MAT274 GCU Week 6 Sample Size Mean and Standard Deviation Quiz Need help getting assignment and quiz completed. Attached is the questions for assignment. P
MAT274 GCU Week 6 Sample Size Mean and Standard Deviation Quiz Need help getting assignment and quiz completed. Attached is the questions for assignment. Please Help!! 1.
/1.17 points
MIntroStat9 12.E.017.
My Notes
Ask Your Teacher
For each of the following situations, identify the response variable and the populations to be
compared, and give I, the n i, and N.
(a) A poultry farmer is interested in reducing the cholesterol level in his marketable
eggs. He wants to compare two different cholesterol-lowering drugs added to the hen’s
standard diet as well as an all-vegetarian diet. He assigns 35 of his hens to each of the
three treatments.
Response variable:
number of marketable eggs laid
egg cholesterol level
caloric intake
number of hens
diet cholesterol level
Populations: (Select all that apply.)
all hens on a farm
hens on a standard diet and receiving one of two cholesterol-lowering drugs
eggs with different cholesterol levels
hens on an all-vegetarian diet
all eggs laid on a farm
I=
n1 =
n2 =
n3 =
N=
(b) A researcher is interested in students’ opinions regarding an additional annual fee
to support non-income-producing varsity sports. Students were asked to rate their
acceptance of this fee on a five-point scale. She received 100 responses, of which 33
were from students who attend varsity football or basketball games only, 20 were from
students who also attend other varsity competitions, and 47 who did not attend any
varsity games.
Response variable:
acceptance rating on a five-point scale
varsity sport played
number of students who attend varsity games
amount of annual fee paid
number of games attended
Populations: (Select all that apply.)
students who do not attend any varsity games
students who attend varsity football or basketball games
students who play sports
students who attend other varsity competitions
students who pay an annual fee
I=
n1 =
n2 =
n3 =
N=
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one
class period, the 45 students were randomly divided into three equal-sized groups, and
each group was taught power calculations from one of the assistants. At the beginning
of the next class, each student took a quiz on power calculations, and these scores
were compared.
Response variable:
number of questions on the quiz
quiz score
rating of the professor on a five-point scale
rating of the assistant on a five-point scale
course grade
Populations: (Select all that apply.)
students passing the course
students who like their TA
students in the three TA groups
all students at the school
the three teaching assistants
I=
n1 =
n2 =
n3 =
N=
2.
/1.17 points
MIntroStat9 12.E.019.
My Notes
Ask Your Teacher
For each of the following situations, give the degrees of freedom for the group (DFG), for error
(DFE), and for the total (DFT). State the null and alternative hypotheses, H 0 and H a, and give
the numerator and denominator degrees of freedom for the F statistic.
(a) A poultry farmer is interested in reducing the cholesterol level in his marketable
eggs. He wants to compare two different cholesterol-lowering drugs added to the hen’s
standard diet as well as an all-vegetarian diet. He assigns 15 of his hens to each of the
three treatments.
DFG =
DFE =
DFT =
H 0:
All groups have the same mean cholesterol level.
The all-vegetarian diet group has a lower mean cholesterol level.
At least one group has a different mean cholesterol level.
The all-vegetarian diet group has a higher mean cholesterol level.
All groups have different mean cholesterol levels.
H a:
The all-vegetarian diet group has a higher mean cholesterol level.
All groups have different mean cholesterol levels.
All groups have the same mean cholesterol level.
At least one group has a different mean cholesterol level.
The all-vegetarian diet group has a lower mean cholesterol level.
numerator df
denominator df
(b) A researcher is interested in students’ opinions regarding an additional annual fee
to support non-income-producing varsity sports. Students were asked to rate their
acceptance of this fee on a seven-point scale. She received 99 responses, of which 30
were from students who attend varsity football or basketball games only, 19 were from
students who also attend other varsity competitions, and 50 who did not attend any
varsity games.
DFG =
DFE =
DFT =
H 0:
At least one group has a different mean rating.
The group of students who do not attend games has a lower mean rating.
All groups have the same mean rating.
All groups have different mean ratings.
The group of students who do not attend games has a higher mean rating.
H a:
At least one group has a different mean rating.
The group of students who do not attend games has a higher mean rating.
The group of students who do not attend games has a lower mean rating.
All groups have the same mean rating.
All groups have different mean ratings.
numerator df
denominator df
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one
class period, the 42 students were randomly divided into three equal-sized groups, and
each group was taught power calculations from one of the assistants. At the beginning
of the next class, each student took a quiz on power calculations, and these scores
were compared.
DFG =
DFE =
DFT =
H 0:
All groups have different mean quiz scores.
All groups have the same mean quiz score.
The group taught by the oldest TA has a higher mean quiz score.
At least one group has a different mean quiz score.
The group taught by the oldest TA has a lower mean quiz score.
H a:
The group taught by the oldest TA has a higher mean quiz score.
The group taught by the oldest TA has a lower mean quiz score.
At least one group has a different mean quiz score.
All groups have different mean quiz scores.
All groups have the same mean quiz score.
numerator df
denominator df
3.
/1.17 points
My Notes
MIntroStat9 12.E.065.
Ask Your Teacher
Many studies have suggested that there is a link between exercise and healthy bones. Exercise
stresses the bones and this causes them to get stronger. One study examined the effect of
jumping on the bone density of growing rats. There were three treatments: a control with no
jumping, a low-jump condition (the jump height was 30 centimeters), and a high-jump
condition (60 centimeters). After 8 weeks of 10 jumps per day, 5 days per week, the bone
3
density of the rats (expressed in mg/cm ) was measured. Here are the data. data173.dat
(a) Make a table giving the sample size, mean, and standard deviation for each group
of rats. Consider whether or not it is reasonable to pool the variances. (Round your
answers for x, s, and
Group
to one decimal place.)
n
s
Control
Low jump
High jump
(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and
P-value. What do you conclude? (Round your test statistic to two decimal places and
your P-value to three decimal places.)
F=
P=
Conclusion: There is —Select— ? statistically significant difference between the three
treatment means at the ? = .05 level.
4.
/1.17 points
MIntroStat9 12.E.516.XP.
My Notes
Ask Your Teacher
A study of reading comprehension in children compared three methods of instruction. The
three methods of instruction are called Basal, DRTA, and Strategies. As is common in such
studies, several pretest variables were measured before any instruction was given. One
purpose of the pretest was to see if the three groups of children were similar in their
comprehension skills. The READING data set described in the Data Appendix gives two pretest
measures that were used in this study. Use one-way ANOVA to analyze these data and write a
summary of your results.
This answer has not been graded yet.
5.
/1.17 points
MIntroStat9 12.E.517.XP.
My Notes
Ask Your Teacher
A study of reading comprehension in children compared three methods of instruction. The
three methods of instruction are called Basal, DRTA, and Strategies. Basal is the traditional
method of teaching, while DRTA and Strategies are two innovative methods based on similar
theoretical considerations. The READING data set includes three response variables that the
new methods were designed to improve. Analyze these variables using ANOVA methods. Be
sure to include multiple comparisons or contrasts as needed. Write a report summarizing your
findings.
This answer has not been graded yet.
/1.17 points
6.
MIntroStat9 12.E.042.
My Notes
Ask Your Teacher
The One-Way ANOVA applet lets you see how the F statistic and the P-value depend on the
variability of the data within groups, the sample size, and the differences among the means.
(a) The black dots are at the means of the three groups. Move these up and down until you get
a configuration that gives a P-value of about 0.01. What is the value of the F statistic?
This answer has not been graded yet.
(b) Now increase the variation within the groups by sliding the standard deviation bar to the
right. Describe what happens to the F statistic and the P-value.
This answer has not been graded yet.
(c)
Using between- and within-group variation, explain why the F statistic and P-value change
in this way.
This answer has not been graded yet.
7.
/1.17 points
My Notes
MIntroStat9 12.E.503.XP.
Ask Your Teacher
Corporate advertising tries to enhance the image of the corporation. A study compared two
ads from two sources, the Wall Street Journal and the National Enquirer. Subjects were asked
to pretend that their company was considering a major investment in Performax, the fictitious
sportswear firm in the ads. Each subject was asked to respond to the question “How
trustworthy was the source in the sportswear company ad for Performax?” on a 7-point scale.
Higher values indicated more trustworthiness. Here is a summary of the results.
Ad source
n
x
s
Wall Street Journal
66
4.77
1.50
National Enquirer
61
2.43
1.64
Find the two-sample pooled t statistic. Then formulate the problem as an ANOVA and report
2
the results of this analysis. Verify that F = t .
This answer has not been graded yet.
8.
/1.17 points
MIntroStat9 12.E.504.XP.
My Notes
Ask Your Teacher
A survey looked at the value of recreational sports on college campuses. One of the questions
asked each student to rate the importance of recreational sports to college satisfaction and
success. Responses were on a 10-point scale with 1 indicating total lack of importance and 10
indicating very high importance. The following table summarizes these results:
Class
n
Mean score
Freshman
730
7.6
Sophomore
535
7.6
Junior
592
7.5
Senior
436
7.3
(a) To compare the mean scores across classes, what are the degrees of freedom for
the ANOVA F statistic?
numerator df
denominator df
(b) The MSG = 9.805. If s p = 2.13, what is the F statistic? (Round your answer to two
decimal places.)
F=
(c) Give an approximate (from Table E) or exact (from software) P-value. (Enter your
answer to four decimal places.)
/1.17 points
9.
My Notes
MIntroStat9 12.E.506.XP.
Ask Your Teacher
Different varieties of the tropical flower Heliconia are fertilized by different species of
hummingbirds. Over time, the lengths of the flowers and the form of the hummingbirds’ beaks
have evolved to match each other. Here are data on the lengths in millimeters of three
varieties of these flowers on the island of Dominica. data378.dat
Do a complete analysis that includes description of the data and a significance test to compare
the mean lengths of the flowers for the three species. (Round your answers for x to four
decimal places, s to three decimal places, and
to three decimal places. Round your test
statistic to two decimal places. Round your P-value to three decimal places.)
flower type
H. bihai
H. caribaea red
H. caribaea yellow
F=
P=
n
s
10.
/1.17 points
MIntroStat9 12.E.511.XP.
My Notes
Ask Your Teacher
Iron-deficiency anemia is the most common form of malnutrition in developing countries,
affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had
traditionally been used in many of these countries, but they have been largely replaced by
aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked
in iron pots will contain more iron than food cooked in other types of pots. One study designed
to investigate this issue compared the iron content of some Ethiopian foods cooked in
aluminum, clay, and iron pots. One of the foods was yesiga wet, beef cut into small pieces and
prepared with several Ethiopian spices. The iron content of four samples of yesiga wet cooked
in each of the three types of pots is given below. The units are milligrams of iron per 100
grams of cooked food. data172.dat
(a) Make a table giving the sample size, mean, and standard deviation for each type of
pot. Is it reasonable to pool the variances? Note that with the small sample sizes in
this experiment, we expect a large amount of variability in the sample standard
deviations.
Type of pot
n
s
Aluminum
Clay
Iron
(b) Run the analysis of variance. Report the F statistic with its degrees of freedom and
P-value. What do you conclude? (Round your test statistic to two decimal places.
Round your P-value to three decimal places.)
F=
P=
Conclusion: There is —Select— ? statistically significant difference between the three
treatment means at the ? = .05 level.
11.
/1.17 points
My Notes
MIntroStat9 13.E.518.XP.
Ask Your Teacher
The National Crime Victimization Survey estimates that there were over 400,000 violent
crimes committed against women by their intimate partner that resulted in physical injury. An
intervention study designed to increase safety behaviors of abused women compared the
effectiveness of six telephone intervention sessions with a control group of abused women who
received standard care. Fifteen different safety behaviors were examined. One of the variables
analyzed was the total number of behaviors (out of 15) that each woman performed. Here is a
summary of the means of this variable at baseline (just before the first telephone call) and at
follow-up 3 and 6 months later.
Time
Group
Baseline 3 months 6 months
Intervention
Control
10.4
12.5
11.9
9.6
9.9
10.4
(a) Find the marginal means. (Round your answers to three decimal places.)
Time
Group
Baseline
Intervention
Control
3 months
6 months
10.4
12.5
11.9
9.6
9.9
10.4
Mean
Mean
Are they useful for understanding the results of this study?
The row means suggest that the intervention group showed more improvement
than the control group.
The row means suggest that the control group showed more improvement than
the baseline group.
The row means suggest that the intervention group showed more improvement
than the 6 months group.
The row means suggest that the control group showed more improvement than
the 3 months group.
The row means suggest that the intervention group showed less improvement
than the control group.
(b) Plot the means. Do you think there is an interaction? Describe the meaning of an
interaction for this study.
Yes there is an interaction, it means that the mean number of actions does not
change over time for the two groups.
Yes there is an interaction, it means that the mean number of actions changes
differently over time for the two groups.
Yes there is an interaction, it means that the mean number of actions changes
consistently over time for the two groups.
No there is not an interaction, meaning that the mean number of actions does
not change over time for the two groups.
(Note: This exercise is from a repeated-measures design, and the data are not
particularly normal because they are counts with values from 1 to 10. Although we
cannot use the methods in this chapter for statistical inference in this setting, the
example does illustrate ideas about interactions.)
12.
/1.17 points
MIntroStat9 13.E.037.
My Notes
Ask Your Teacher
The amount of chromium in the diet has an effect on the way the body processes insulin. In an
experiment designed to study this phenomenon, four diets were fed to male rats. There were
two factors. Chromium had two levels: low (L) and normal (N). The rats were allowed to eat as
much as they wanted (M) or the total amount that they could eat was restricted (R). We call
the second factor Eat. One of the variables measured was the amount of an enzyme called
GITH. The means for this response variable appear in the following table.
Eat
Chromium
M
R
L
4.545 5.175
N
4.425 5.317
A plot of the mean GITH for these diets, with the factor Chromium on the x axis and GITH on
the y axis is given below. For each Eat group the points for the two Chromium means are
connected.
(a) Describe the patterns you see. Does the amount of chromium in the diet appear to
affect the GITH mean? Does restricting the diet rather than letting the rats eat as
much as they want appear to have an effect? Is there an interaction?
This answer has not been graded yet.
(b) Compute the marginal means. Compute the differences between the M and R diets
for each level of Chromium. Use this information to summarize numerically the
patterns in the plot.
This answer has not been graded yet.
/1.17 points
13.
My Notes
MIntroStat9 13.E.040.
Ask Your Teacher
Iron-deficiency anemia is the most common form of malnutrition in developing countries,
affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had
traditionally been used in many of these countries, but they have been largely replaced by
aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked
in iron pots will contain more iron than food cooked in other types of pots. One study designed
to investigate this issue compared the iron content of some Ethiopian foods cooked in
aluminum, clay, and iron pots. Foods considered were yesiga wet’, beef cut into small pieces
and prepared with several Ethiopian spices; shiro wet’, a legume-based mixture of chickpea
flour and Ethiopian spiced pepper; and ye-atkilt allych’a, a lightly spiced vegetable casserole.
Four samples of each food were cooked in each type of pot. The iron in the food is measured in
milligrams of iron per 100 grams of cooked food. The data are shown in the table below.
Iron Content (mg/100 g) of Food Cooked in Different Pots
Type of pot
Meat
Legumes
Vegetables
Aluminum
1.77 2.36 1.96 2.14 2.40 2.17 2.41 2.34 1.03 1.53 1.07 1.30
Clay
2.27 1.28 2.48 2.68 2.41 2.43 2.57 2.48 1.55 0.79 1.68 1.82
Iron
5.27 5.17 4.06 4.22 3.69 3.43 3.84 3.72 2.45 2.99 2.80 2.92
(a) Make a table giving the sample size, mean, and standard deviation for each type of
pot. Is it reasonable to pool the variances? Although the standard deviations vary more
than we would like, this is partially due to the small sample sizes, and we will proceed
with the analysis of variance.
This answer has not been graded yet.
(b) Plot the means. Give a short summary of how the iron content of foods depends
upon the cooking pot.
This answer has not been graded yet.
(c) Run the analysis of variance. Give the ANOVA table, the F statistics with degrees of
freedom and P-values, and your conclusions regarding the hypotheses about main
effects and interactions.
This answer has not been graded yet.
14.
/1.17 points
was MIntroStat9 13.E.045.
My Notes
Ask Your Teacher
Do left-handed people live shorter lives than right-handed people? A study of this question
examined a sample of 949 death records and contacted next of kin to determine handedness.
Note that there are many possible definitions of “left-handed.” The researchers examined the
effects of different definitions on the results of their analysis and found that their conclusions
were not sensitive to the exact definition used. For the results presented here, people were
defined to be right-handed if they wrote, drew, and threw a ball with the right hand. All others
were defined to be left-handed. People were classified by sex (female or male) and handedness
(left or right), and a 2 ? 2 ANOVA was r…
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