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:
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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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.
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