D.Rose Mat 274 Project
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School
Grand Canyon University *
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Course
274
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
Pages
6
Uploaded by DoctorBarracuda2548
Dyane Rose
20835047
MAT 274 BENCHMARK FORMAT AND STYLE TEMPLATE
1.
For each part, of the required area under the normal curve. In addition, include a screenshot of your Excel computation to find this area. a.
Insert screenshot and figure for part (a)
Given Data Value (x)
Data Value (x)
140
Mean
147
Standard Deviation
8
Sample Size (default 1)
1
Z-Score
-0.875
Left Probability P(x<a)
0.19078695
3
Right Probability P(x>a)
0.80921304
7
b.
Insert screenshot and figure for part (b)
Given Data Value (x)
Data Value (x)
140
Mean
147
Standard Deviation
8
Sample Size (default 1)
8
Z-Score
-
2.47487373
4
Left Probability P(x<a)
0.00666416
4
Right Probability P(x>a)
0.99333583
6
c.
Insert screenshot and figure for part (c)
2.
Given Data Value (x)
Data Value (x)
140
Mean
147
Standard Deviation
8
Sample Size (default 1)
11
Z-Score
-
2.90204669
2
Left Probability P(x<a)
0.00185366
6
Right Probability P(x>a)
0.99814633
4
d.
Comment on the relationship among the probabilities in parts (a),(b), and (c). As the sample size gets higher, the probability will also increase. There is a direct relationship between the two. The right probability increases because there is a greater amount of chances the group has in getting diabetes. 2.
Insert a conditional probability table here, then answer the questions in each art below. Positive Test Result
Negative Test Result
Total
Has Diabetes
6790
210
7000
No Diabetes
10230
82,770
93,000
a.
Answer part (a) here. 6,790
b.
Answer part (b) here. 6790/(6790+10230)= 0.3989
c.
Answer part (c) here. 210
d.
Answer part (d) here. 210/(210+82770)=0.00253
e.
Comment on how prevalence of the disease affects your ability to trust the test. Discuss what factors would lead you to trust the blood test, or not trust the blood test.
Based on the prevalence of the disease, I do not trust the test because the probability of having
the disease given that the person tested positive is too low of a number. In order for me to trust it the number will have to be much higher than what it is as it will ensure the effectiveness
of the test. 3.
Answer each part below.
a.
Detailed experimental design should include the type of experiment, how you chose your sample size, what data is being collected, and how you would collect that data. Experimental design statistics involves the design and analysis of experiments. It is also when an
experiment is performed in a structured way so that the most accurate results can be a useful tool to the hypothesis of the experiment. There are various ways to choose your sample size, this includes by effect size, population standard deviation, postulated effect, and the significance level. The data that is being collected is the glucose levels of patients. Blood sample
is obtained from the patients. Blood is taken from the patients by firstly asking the patient to
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open his/her hand, palm facing up. This technique will allow the person to be able to reach the desired spot. The next step would be to take the base of the squeeze it, while squeezing take a lancet to prick the finger. Next, take a small quantity of the blood and place it onto a test strip. Once the strip is placed in a meter, the results will show.
z Find Sample Size (given σ)
Pop. STDEV (σ)
5
Margin of Error
2.8
Confidence Level
0.98
z*
2.326347874
Sample Size (n)
18
B.Remember to discuss how you would randomize for sampling and assignment, what type of randomization are you using? Ideally I would do a simple random sampling, however due to me not having direct access to the patient’s blood I would have use a hypothetical data set provided by the instructor. 135
139
146
144
144
148
143
142
139
146
148
140
140
144
144
150
150
146
C. Include type of test used, number of tails, and a justification for this choice. The type of test that was used in this experiment would be the mean t significance test. This type of test is preferred over the other options because the sample size is large and it is able to provide average number of patients that would be above 140, which means in this experiment we would be looking at the right tail. d.Make sure to include correct statistical notation for the formal null and alternative, do not just state this in words. Typeequationhere.
H0: u=140
H1:u>140
e.State and discuss your chosen confidence level, why this is appropriate, and interpret the lower and upper limits. I am 98% confident that the mean glucose levels of patients lies between 141 and 146. It is appropriate because both limits are above 140 which is what we are trying to find. Using this information it is said that I do have sufficient evidence.
f.
State your significance level, interpret your p-value, and make a decision on the null. We used 0.01 as the significance level because we are in a medical setting. Since my P-value is
less than my alpha 0.01, I will reject the null hypothesis. Because I reject my null hypothesis
there is sufficient evidence that my patient does have diabetes.
t Significance Test (1-sample)
Hypothesized Value
140
Sample mean (
)
x̄
143.7777778
Sample STDEV (s)
4.080881617
n
18
Significance Level
0.01
t-statistic
3.92752236
P-value left-tail
0.999457524
P-value right-tail
0.000542476
P-value two-tail
0.001084952
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