6. Two-tailed hypothesis testing - Step by step S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have an effect on depression symptoms. Suppose that a researcher is interested in testing SAM-e on patients who are struggling with HIV. He obtains a sample of n = 20 patients and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes the Beck Depression Inventory (BDI), which is a 21-item, multiple-choice self-report inventory for measuring the severity of depression. The scores from the sample produced a mean of M= 27.9 with a standard deviation of s= 3.20. In the general population of HIV patients, the standardized test is known to have a population mean of u 30.3. Because there are no previous studies using SAM-e with this population, the researcher doesn't know how it will affect these patients; therefore, he uses a two-tailed single-sample t test to test the hypothesis. From the following, select the correct null and alternative hypotheses for this study: OH: MSAM-e 2 30.3; H₁: MSAM-e> 30.3 OH: USAM- 30.3; H₁: USAM-e 30.3 OH: USAM- S 30.3; H₁: USAM-e> 30.3 OH,: MSAM-e 2 30.3; H₁: MSAM-e < 30.3 Assume that the depression scores among patients taking SAM-e are normally distributed. You will first need to determine the degrees of freedom. There are degrees of freedom. Use the t distribution table to find the critical region for a = 0.01. The t Distribution:
6. Two-tailed hypothesis testing - Step by step S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have an effect on depression symptoms. Suppose that a researcher is interested in testing SAM-e on patients who are struggling with HIV. He obtains a sample of n = 20 patients and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes the Beck Depression Inventory (BDI), which is a 21-item, multiple-choice self-report inventory for measuring the severity of depression. The scores from the sample produced a mean of M= 27.9 with a standard deviation of s= 3.20. In the general population of HIV patients, the standardized test is known to have a population mean of u 30.3. Because there are no previous studies using SAM-e with this population, the researcher doesn't know how it will affect these patients; therefore, he uses a two-tailed single-sample t test to test the hypothesis. From the following, select the correct null and alternative hypotheses for this study: OH: MSAM-e 2 30.3; H₁: MSAM-e> 30.3 OH: USAM- 30.3; H₁: USAM-e 30.3 OH: USAM- S 30.3; H₁: USAM-e> 30.3 OH,: MSAM-e 2 30.3; H₁: MSAM-e < 30.3 Assume that the depression scores among patients taking SAM-e are normally distributed. You will first need to determine the degrees of freedom. There are degrees of freedom. Use the t distribution table to find the critical region for a = 0.01. The t Distribution:
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
Can you please help me with this problem . I have been trying to solve this three days ago and still confused
Transcribed Image Text:6. Two-tailed hypothesis testing - Step by step
S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have an effect on depression symptoms. Suppose
that a researcher is interested in testing SAM-e on patients who are struggling with HIV. He obtains a sample of n = 20 patients and asks each person
to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes the Beck Depression Inventory (BDI),
which is a 21-item, multiple-choice self-report inventory for measuring the severity of depression.
The scores from the sample produced a mean of M= 27.9 with a standard deviation of s= 3.20. In the general population of HIV patients, the
standardized test is known to have a population mean of u = 30.3. Because there are no previous studies using SAM-e with this population, the
researcher doesn't know how it will affect these patients; therefore, he uses a two-tailed single-sample t test to test the hypothesis.
From the following, select the correct null and alternative hypotheses for this study:
OH,: MSAM-e ≥ 30.3; H₁: MSAM-e> 30.3
OH, USAM-e = 30.3; H₁: USAM-e 30.3
OH: USAM-e 30.3; H₁: USAM-e> 30.3
OH: MSAM-e 2 30.3; H₁: MSAM-e < 30.3
Assume that the depression scores among patients taking SAM-e are normally distributed. You will first need to determine the degrees of freedom.
There are
degrees of freedom.
Use the t distribution table to find the critical region for a = 0.01.
The t Distribution:
Proportion in One Tail
Transcribed Image Text:There are
Use the t distribution table to find the critical region for a = 0.01.
The t Distribution:
df
1
2
3
4
5
6
7
8
9
10
11
12
13
88NNNN
26
27
28
29
30
40
60
14
15
16
17
0.689 1.333
18
0.688 1.330
19 0.688 1.328
20
1.325
1.725
2.086
2.845
0.687
0.686 1.323
21
1.721
2.080
2.831
22 0.686 1.321 1.717
2.074 2.508
2.819
2.069
2.807
23 0.685 1.319 1.714
24 0.685 1.318 1.711
25
2.064
2.797
0.684 1.316 1.708
2.060
2.485
2.787
2.479
2.056
2.779
2.052 2.473 2.771
0.684 1.315 1.706
0.684 1.314 1.703
1.701 2.048
1.699
2.467
2.763
0.683 1.313
0.683 1.311
2.045 2.462
2.756
0.683
2.042
2.457 2.750
0.681
2.021
2.704
1.310 1.697
1.303 1.684
0.679 1.296 1.671 2,000
0.677 1.289 1.658 1.980
0.674 1.282
2.660
2.617
1.645
2.576
120
00
0.25
Proportion in One Tail
0.10 0.05 0.025 0.01
Proportion in Two Tails Combined
0.20 0.10 0.05
0.02
3.078 6.314 12.706
31.821
63.657
0.816 1.886 2.920 4.303 6.965
9.925
0.765 1.638 2.353
3.182 4.541
5.841
0.741 1.533 2.132
2.776 3.747
4.604
0.727 1.476
2.015 2.571 3.365 4.032
0.718 1.440
0.711 1.415
0.706
0.50
1.000
degrees of freedom.
2.447
3.143
3.707
1.943
1.895
2.365 2.998 3.499
1.397 1.860
2.306 2.896
3.355
0.703 1.383 1.833
2.262
2.821
3.250
0.700 1.372 1.812 2.228 2.764
3.169
0.697 1.363
1.796 2.201 2.718 3.106
3.055
0.695 1.356 1.782 2.179 2.681
0.694 1.350 1.771 2.160 2.650
3.012
0.692
1.345 1.761 2.145 2.624 2.977
0.691 1.341 1.753 2.131 2.602 2.947
0.690 1.337 1.746 2.120 2.583 2.921
2.110 2.567
1.734 2.101 2.552 2.878
2.898
1.729 2.093 2.539
2.861
Thet statistic is
The estimated standard error is
The t statistic
1.740
Y
Therefore, the researcher
2.528
0.005
2.518
0.01
2.500
2.492
The critical t scores (the values that define the borders of the critical region) are
2.423
2.390
2.358
2.326
1.960
in the critical region. Therefore, the null hypothesis
rejected.
conclude that SAM-e has a significant effect on the moods of HIV patients.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Step 1: Mentioning the given data
VIEWStep 2: Determining hypothesis
VIEWStep 3: Computing df
VIEWStep 4: Computing the critical region
VIEWStep 5: Computing critical values
VIEWStep 6: Computing the standard error
VIEWStep 7: Computing test statistic
VIEWStep 8: Stating decision
VIEWStep 9: Stating conclusion
VIEWSolution
VIEW
Trending now
This is a popular solution!
Step by step
Solved in 10 steps with 14 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman