Running Head: HYPOTHESIS TESTING AND CONFIDENCE INTERVALS 1
Hypothesis Testing And Confidence Intervals
Name
Institutional Affiliation
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
Project Part B: Hypothesis Testing and Confidence Intervals
a) the average (mean) level of glucose is less than 130
Null Hypothesis: the average (mean) level of glucose was greater than or equal to 130
H₀: µ > 130
Alternate Hypothesis: the average level of glucose was less than 130
Ha: µ > 130
Analysis plan: Significance Level, α=0.05
As the sample size, n > 30 then a z-test is used for mean to test the given hypothesis
Since the alternative hypothesis is Ha: µ > 130, then the given test would be one-tailed z-test
Critical Value and Decision Rule:
The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645.
Decision Rule: Reject H₀, if z – statistic, -1.645
Rejection region: z < -1.645 or z > 1.645, which corresponds to α = 0.05.
Test Statistic:
xˉ = 114.6
S= 35.92
μ0= 130
n=40
2
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
3
Z= 114.6-130 = -2.71
Find out the probability of the Z being greater than the test statistic. Since the Ha is a greater than
hypothesis, then the p-value is calculated as follows:
p= ( 1-corresponding Z value)
p=( 1- 0.00336)
p= 0.99664
Interpretation and Conclusion
The numerical value does not fall within the rejection region. The test statistic shows that the
null hypothesis should not be rejected because the significant evidence at α=0.05 depicts that the
mean of the glucose is less than 130.
b) The true population proportion of number somewhat satisfied with their hospital stay is
greater than 28%,
Null hypothesis: true population satisfied with hospital stay is greater than 28%
H₀: p > 0.28
Alternative hypothesis: the population in proportion is less than 28%
Ha: p < 0.28
Z= 0.28-0.25
(0.25*0-75)/40
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
4
= 0.4381
P value of p (z>z)
1-p ( 2>0.4381
1 – p= 0.33
p- 1-0.33= 0.77
Interpretation and conclusion
The null hypothesis is accepted and the population is satisfied with the hospital stay. There is
sufficient evidence at 0.77 level of significant is greater than 0.28 to indicate that the population
is satisfied with hospital stay.
c) The average (mean) score on the diabetes pretest is greater than 52.
Null hypothesis: the average (mean) score on the diabetes pretest is greater than 52
H₀: µ > 52
Alternative hypothesis: the average (mean) score on the diabetes pretest is less than 52
Ha: µ < 52
Select the appropriate test statistic:
Since the sample size, n is greater than 30 (n< 30),a z-test is used for mean to test the given
hypothesis
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
5
Ha is a less than alternative, therefore
Decision rule:
The H₀ will be rejected if p< 0.05 and accept it if p≥ 0.05
xˉ = 50.25
μ0 = 52
S= 18.22
n= 40
Z= 50.25-52 =
18.22/
-1.75 = -0.6076
2.88
Find the p-value in the Z-table. In this case the p-value is the value that corresponds to the z test,
because the Ha is a less than alternative hypothesis
-0.6076 correspond to 0.27425
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
6
The p-value is -0.27425
Interpretation and Conclusion
The rejection rule states that H₀ will be rejected if p< 0.05 and accept it if p≥ 0.05. The null
hypothesis is rejected because the value of p, -0.27425 is less than the significant level, α=0.05
d) The average (mean) score on the diabetes posttest ONLY among those that are "somewhat
satisfied" is less than 75.
Null hypothesis: the average score on the diabetes posttest for the somewhat satisfied is less than
75
H₀: µ < 75
Alternative hypothesis: the average (mean) score on the diabetes posttest for the somewhat
satisfied is greater than 75
Ha: µ > 75
Analysis plan: Significance Level, α=0.05
As the sample size, n > 30 then a z-test is used for mean to test the given hypothesis
Since the alternative hypothesis is Ha: µ > 75, then the given test would be one-tailed z-test
Critical Value and Decision Rule:
The critical value for significance level, α=0.05 for a lower-tailed z-test is given as-1.645.
Decision Rule: Reject H₀, if z – statistic, -1.645
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
7
Test Statistic:
Rejection region: z < -1.645 or z > 1.645, which corresponds to α = 0.05.
xˉ = 50.9
μ0 = 72
S= 25.13
n= 40
Z= 50.9 – 72
25.13/
= -21.1 = -5. 359
3.937
Interpretation and conclusion
The test statistic does not lie within the rejection region. It should there be accepted and used in
the research. Also, the significant evidence at α=0.05 clearly indicates that the average score on
the diabetes posttest ONLY among those that are "somewhat satisfied" is less than 75. This
complies with the manager’s speculation.
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
8
Summary report
The hypothesis tests carried out on the proposed speculations is of great importance. The
tests show that some of the speculations ought to be improved while others fit the study. The
thought about the average (mean) level of glucose being less than 130 is correct and ought to be
considered. From the test that was carried out, it is true that the average is less than 130.
According to the test carried out, the selected population is comfortable with staying at the
hospital. The proposed idea that the true population proportion of number somewhat satisfied with
their hospital stay is greater than 28%, turned out to be true, as the test results showed that 77% is
satisfied with the hospital stay. The speculation is therefore true according to the manager.
It is essential to note that the speculation concerning the diabetes pretest is not supported
because it was rejected by the hypothesis test. The average score for on the diabetes pretest turned
out to be less than the given number, 52.
The speculation concerning the mean score for the individuals who were somewhat
satisfied by the diabetes posttest is correct according to the test results. The manager should hold
on to the thought during the research. It is important to aim at getting a greater number of
individuals who are satisfied by the posttest.
HYPOTHESIS TESTING AND CONFIDENCE INTERVALS
Appendices
Appendix 1: Steps in hypothesis testing
1. Null hypothesis(H0)
2. Alternative (research) hypothesis (Ha)
3. Test statistic:
4. Rejection region
5. Assumptions
6. Experiment and calculation of test statistic
7. Conclusion
Appendix 2: Confidence intervals
9
Hosp_Stay
2
3
1
1
7
7
8
8
9
4
1
1
6
8
7
6
1
8
6
6
1
5
2
2
3
1
4
4
5
4
8
6
8
9
9
8
5
7
7
3
Hosp_Satisfaction
VeryDissat
SWDissat
SWSat
SWSat
SWDissat
VerySat
SWDissat
VerySat
SWSat
SWDissat
SWSat
VerySat
VeryDissat
SWDissat
SWDissat
SWDissat
VerySat
VerySat
SWDissat
SWDissat
VerySat
VerySat
VeryDissat
VeryDissat
VerySat
SWDissat
SWDissat
SWDissat
VeryDissat
SWSat
VeryDissat
VeryDissat
SWDissat
SWSat
VerySat
SWSat
SWSat
SWSat
VeryDissat
SWSat
Diab_Pretest
34
33
29
17
69
69
81
81
52
45
38
27
45
58
68
48
9
50
65
64
25
50
47
24
35
29
39
53
57
50
64
90
52
52
67
68
67
44
57
58
Diab_Posttest
39
30
22
14
60
70
82
88
100
48
28
33
54
71
84
49
15
51
51
78
30
45
41
18
30
31
33
42
49
50
100
95
63
64
77
68
60
53
51
50
Glucose
122
116
108
63
74
84
67
57
231
93
76
163
217
112
107
95
104
63
189
53
96
102
142
133
88
87
161
104
92
168
72
100
63
132
171
163
84
102
130
71
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Course Project: Hospital Stays, Impact of Education, Health Data
Introduction | PROJECT PART A: Exploratory Data Analysis | Project Part A: Grading Rubric | Project Part B:
Hypothesis Testing and Confidence Intervals | Project Part B: Grading Rubric | Project Part C: Regression and
Correlation Analysis | Project Part C: Grading Rubric
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Introduction
In this case, 40 individuals visited the hospital looking for information and education regarding their diabetes.
Since diabetes relates to the body’s ability to use glucose, their glucose level was measured. These patience
took a knowledge test about diabetes before and after being given some educational materials. Satisfaction
with their overall visit was also measured through a survey. The data appear below for your reference. The
Excel spreadsheet with these data can be found in Doc Sharing and should be opened in Minitab to complete
the analyses required in each part of this project.
Hosp_Stay
Hosp_Satisfaction Diab_Pretest
Diab_Posttest
Glucose
2
VeryDissat
34
39
122
3
SWDissat
33
30
116
1
SWSat
29
22
108
1
SWSat
17
14
63
7
SWDissat
69
60
74
7
VerySat
69
70
84
8
SWDissat
81
82
67
8
VerySat
81
88
57
9
SWSat
52
100
231
4
SWDissat
45
48
93
1
SWSat
38
28
76
1
VerySat
27
33
163
6
VeryDissat
45
54
217
8
SWDissat
58
71
112
7
SWDissat
68
84
107
6
SWDissat
48
49
95
1
VerySat
9
15
104
8
VerySat
50
51
63
6
SWDissat
65
51
189
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SWDissat
64
78
53
1
VerySat
25
30
96
5
VerySat
50
45
102
2
VeryDissat
47
41
142
2
VeryDissat
24
18
133
3
VerySat
35
30
88
1
SWDissat
29
31
87
4
SWDissat
39
33
161
4
SWDissat
53
42
104
5
VeryDissat
57
49
92
4
SWSat
50
50
168
8
VeryDissat
64
100
72
6
VeryDissat
90
95
100
8
SWDissat
52
63
63
9
SWSat
52
64
132
9
VerySat
67
77
171
8
SWSat
68
68
163
5
SWSat
67
60
84
7
SWSat
44
53
102
7
VeryDissat
57
51
130
3
SWSat
58
50
71
The variables are
1. Hospital stay – number of days in hospital
2. Hospital satisfaction – level of satisfaction with hospital services during stay (very highly satisfied, highly
satisfied, somewhat dissatisfied, and very dissatisfied)
3. Diabetes Pretest – score on diabetes knowledge test (must score 95 or higher to leave)
4. Diabetes Posttest – score on diabetes knowledge test after receiving educational material created for
this study
5. Glucose – blood glucose in mg/dL.
The data are available in Doc Sharing Course Project Data Set as an Excel file. You are to copy and paste
the data set into a Minitab Worksheet.
PROJECT PART A: Exploratory Data Analysis
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Open the file MATH533_Course_Project_Data_HOSPITAL.xlsx from Doc Sharing.
Summarize the data for each of the five variables. For each variable, find the mean, median, variance,
and standard deviation. Use Minitab as appropriate, and explain what the results mean. These
calculations may not be possible for each variable. If you cannot calculate any or all of these for a
specific variable, please note that and state why.
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Analyze the connections or relationships between two variables. There are ten pairings possible here
(Hospital stay and hospital satisfaction, hospital stay and diabetes pretest, hospital stay and diabetes
posttest, hospital stay and glucose, hospital satisfaction and diabetes pretest, hospital satisfaction and
diabetes posttest, hospital satisfaction and glucose, diabetes pretest and diabetes posttest, diabetes
pretest and glucose, and diabetes posttest and glucose ). Choose two of these pairings and find the
correlation coefficient and show the scatter plot. Explain what you see. Some variables show clear
relationships, while others do not.
Prepare your report in Microsoft Word (or some other word processing package), integrating your
graphs and tables with text explanations and interpretations. Be sure that you have graphical and
numerical back up for your explanations and interpretations. Be selective in what you include in the
report. You should not generate a 20 page report on every variable and every possible relationship.
Rather what you should do is to highlight what you see for the individual and two or three sentences of
interpretation. For the two pairings you selected, identify and report your results using graphical and
numerical summary (as appropriate), with interpretations.
All DeVry University policies are in effect, including the plagiarism policy.
Project Part A report is due by the end of Week 2.
Project Part A is worth 100 total points. See grading rubric below.
Submission: The report from part 4 including all relevant graphs and numerical analysis along with
interpretations.
Format for report:
A. Brief Introduction
B. Discuss your 1st individual variable
C. Discuss your 2nd individual variable
D. Discuss your 3rd individual variable
E. Discuss your 4th individual variable
F. Discuss your 5th individual variable
G. Discuss your 1st pairing of variables
H. Discuss your 2nd pairing of variables
I. Conclusion
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Project Part A: Grading Rubric
Category
Points
%
Description
Five Individual Variables
- 12pts. each
60
60
graphical analysis, numerical analysis (when
appropriate) and interpretation
Two Relationships - 15
pts. each
30
30
graphical analysis, numerical analysis (when
appropriate) and interpretation
Communication Skills
10
10
writing, grammar, clarity, logic, cohesiveness,
adherence to the above format
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Category
Points
%
Description
Total
100
100
A quality paper will meet or exceed all of the
above requirements.
Project Part B: Hypothesis Testing and Confidence Intervals
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Your manager has speculated the following:
a. the average (mean) level of glucose is less than 130
b. the true population proportion of number somewhat satisfied with their hospital stay is greater than 28%,
c. the average (mean) score on the diabetes pretest is greater than 52.
d. the average (mean) score on the diabetes posttest ONLY among those that are "somewhat satisfied" is
less than 75.
1. Using the sample data, perform the hypothesis test for each of the above situations in order to
see if there is evidence to support your manager’s belief in each case a.-d. In each case use the
Seven Elements of a Test of Hypothesis, in Section 6.2 of your textbook with α = .05, and explain
your conclusion in simple terms. Also be sure to compute the p-value and interpret.
2. Follow this up with computing 95% confidence intervals for Glucose and Diabetes Posttest, and
again interpreting these intervals.
3. Write a report to your manager about the results, distilling down the results in a way that would be
understandable to someone who does not know statistics. Clear explanations and interpretations
are critical.
All DeVry University policies are in effect, including the plagiarism policy.
Project Part B report is due by the end of Week 6.
Project Part B is worth 100 total points. See grading rubric below.
Submission: The report from part 3 + all of the relevant work done in the hypothesis testing (including
Minitab) in 1, and the confidence intervals (Minitab) in 2 as an appendix.
Format for report:
A. Summary Report (about 1 paragraph on each of the speculations a.-d.)
B. Appendix with all of the steps in hypothesis testing (the format of the Seven Elements of a Test of
Hypothesis, in Section 6.2 of your textbook) for each speculation a.-d. as well as the confidence
intervals, and including all Minitab output
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Project Part B: Grading Rubric
Category
Points
%
Description
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Category
Points
%
Description
Addressing each
speculation - 20 pts.
each
80
80
hypothesis test, interpretation, confidence
interval (where applicable) and interpretation
Summary report
20
20
1 paragraph on each of the speculations
Total
100
100
A quality paper will meet or exceed all of the
above requirements.
Project Part C: Regression and Correlation Analysis
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Using Minitab perform the regression and correlation analysis for the data on diabetes posttest (Y), the
dependent variable, and diabetes pretest (X), the independent variable, by answering the following.
1. Generate a scatterplot for diabetes posttest (Y) vs. diabetes pretest (X) including the graph of the "best
fit" line. Interpret.
2. Determine the equation of the "best fit" line, which describes the relationship between diabetes posttest
and diabetes pretest.
3. Determine the coefficient of correlation. Interpret.
4. Determine the coefficient of determination. Interpret.
5. Test the utility of this regression model (use a two tail test with α =.05). Interpret your results, including
the p-value.
6. Based on your findings in 1-5, what is your opinion about using diabetes pretest to predict diabetes
postest? Explain.
7. Compute the 95% confidence interval for beta-1 (the population slope). Interpret this interval. In an
attempt to improve the model, we attempt to do a multiple regression model predicting diabetes posttest
based on diabetes pretest and glucose.
8. Using Minitab, run the multiple regression analysis using the variables diabetes pretest and glucose to
predict diabetes posttest. State the equation for this multiple regression model.
9. Perform the Global Test for Utility (F-Test). Explain your conclusion.
10. Perform the t-test on each independent variable. Explain your conclusions and clearly state how you
should proceed. In particular, which independent variables should we keep and which should be
discarded.
11. Is this multiple regression model better than the linear model that we generated in parts 1-7? Explain.
All DeVry University policies are in effect, including the plagiarism policy.
Project Part C report is due by the end of Week 7.
Project Part C is worth 100 total points. See grading rubric below.
Summarize your results from 1-11 in a report that is three pages or less in length and explains and
interprets the results in ways that are understandable to someone who does not know statistics.
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Submission: The summary report + all of the work done in 1-11 (Minitab Output + interpretations) as an
appendix.
Format:
A. Summary Report
B. Points 1-11 addressed with appropriate output, graphs and interpretations. Be sure to number each
point 1-11.
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Project Part C: Grading Rubric
Category
Questions 1 - 9 and 11,
are worth 6.5 pts. each
Question 10
Summary
Total
Points
65
15
20
100
%
Description
65
addressed with
appropriate output,
graphs and
interpretations
15
addressed with
appropriate output,
graphs and
interpretations
20
writing, grammar,
clarity, logic, and
cohesiveness
100
A quality paper will
meet or exceed all
of the above
requirements.
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