School

Quinnipiac University **We aren't endorsed by this school

Course

MA 585

Subject

Statistics

Date

Aug 23, 2023

Pages

3

Uploaded by JusticeRook30236 on coursehero.com

Julia Bala
Eleanor Vogelsang
Grace Hughes
PROJECT 4
Estimation of the Population Mean of Soft Plaque Deposit (Confidence Interval of the
Mean). Estimation of the Population Proportion of Soft Plaque Deposit (Confidence
Interval of the Proportion).
This project uses the sample data of the experiment Atassi (A-1), shown here. Assume the variable, soft
plaque deposit index, is approximately normally distributed.
In a study of the oral home care practice and reasons for seeking dental care among individuals
on renal dialysis, Atassi (A-1) studied 90 subjects on renal dialysis. The oral hygiene status of all
subjects was examined using a plaque index with a range of 0 to 3 (0=no soft plaque deposits,
3=an abundance of soft plaque deposits). The following table shows the plaque index scores for
all 90 subjects.
1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50;
1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00;
2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00;
2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00;
1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17;
2.17; 2.00; 2.17; 2.00; 2.17;
This project has two parts.
Part I. Confidence Interval on the Mean.
Show the sample data. Describe the purpose for computing a confidence interval for the mean.
(What you are setting out to find) Pick a confidence level of your choice.
1.
Compute a sample mean.
163.55
90
=
1.8172
2.
Describe the variable.
The variable used is the mean soft plaque deposited index or the average of sample soft
plaque deposite index which uses the 1-3 value. 0 being no soft plaque deposite and 3
being an abundance of soft plaque depostie.
3.
Describe the confidence level you are taking and its specific meaning.

Chosen confidence level:
α
=
0.05
95% confidence level, meaning 95% of the time estimates of the interval of sample mean
will include the population mean.
4.
Show the confidence interval formula that you are using.
μ±z
√
s
2
n
μ
=
mean
s
=
sample SD
n
=
sample
¿¿
z
=
valuedetermined by condifencelevel found
¿
z distributiontable
5.
Show the reliability coefficient (critical value).
Critical value= 1.96 for 95% confidence interval obtained from z distribution table
6.
Show all the pertinent computations using the equation editor.
confidenceinterval
=
1.8172
±
1.96
√
0.562548
2
90
=(
1.7010,1.9335
)
7.
Draw a conclusion in the context of the experiment.
The average of oral hygiene status of all subjects lies between
1.7010
∧
1.9335
at a 95%
chance.
Part II. Confidence Interval on the Proportion.
Show the sample data. Describe the purpose for computing a confidence interval on the
Proportion (What you are setting out to obtain) Pick a confidence level of your choice.
1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50;
1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00;
2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00;
2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00;
1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17;
2.17; 2.00; 2.17; 2.00; 2.17;
1.
Compute a sample proportion of your choice (pick a certain index, count how many
times it comes up in the sample, divide this frequency by sample size).
Certain index= 2.00, Frequency= 18, Sample size= 90

p
=
18
90
=
0.20
2.
Describe the variable.
The variable used is the proportion of soft plaque deposit index which is also the proportion
sample of the soft plaque deposit index.
3.
Describe the confidence level you are taking and its specific meaning.
Chosen confidence level:
α
=
.90
The confidence coefficient (same to confidence level) of 0.90 means there's a 90% confidence
level therefore indicating that there is a 10% chance of being wrong. Meaning that there is a
90% chance of the time estimates of the interval of sample proportion will include the population
mean.
4.
Show the confidence interval formula that you are using. (p.s. couldn't get the p^ to
insert correctly so below is what I got)
1
−
p
^
¿
¿
phat
¿
¿
Confidence Interval
=
p
^
± z
√
¿
5.
Show the reliability coefficient (critical value).
Critical value= 1.65 for 90% confidence interval.
6.
Show all the pertinent computations using the equation editor.
ConfidenceInterval
=
0.2
±
1.65
√
0.2
(
1
−
0.2
)
90
= (0.1304 ,0.2696)
7.
Draw a conclusion in the context of the experiment.
The average proportion of soft plaque deposit index lies between 0.1304 and 0.2696 at a 90%
chance.
A grade level A implies:
a
. your project presents in full all the requirements of part I & part II; Attach the text and data of
the research. You must provide your answers with all the applicable computations, formatted as
word.doc using equation editor. You must answer the question(s) raised by this research. Each
answer must be complete and correct
.
b. you submit your project on time;

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