S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have an effect on depression symptoms.
S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have an effect on depression symptoms.
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Transcribed Image Text:5. 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 cancer. She obtains a sample of n = 30 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 = 26.2 with a standard deviation of s = 2.97. In the general population of cancer patients, the
standardized test is known to have a population mean of μ = 28.1. Because there are no previous studies using SAM-e with this population, the
researcher doesn't know how it will affect these patients; therefore, she 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:
Ho: USAM-e * 28.1; H₁: USAM-e = 28.1
O Ho: USAM-e ≤28.1; H₁: USAM-e > 28.1
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.
Ho: USAM-e = 28.1; H₁: USAM-e * 28.1
Use the t distribution table to find the critical region for a = 0.05.
Ho: USAM-e 2 28.1; H₁: USAM-e < 28.1
The t Distribution:
4
Proportion in One Tail
0.10 0.05 0.025 0.01 0.005
Proportion in Two Tails Combined
df
0.50
0.20 0.10 0.05 0.02
0.01
63.657
1 1.000 3.078 6.314 12.706 31.821
2
0.816 1.886
6.965 9.925
3
2.920 4.303
0.765 1.638 2.353 3.182 4.541
0.741 1.533 2.132 2.776 3.747
5.841
4.604
0.727 1.476 2.015 2.571 3.365 4.032
0.718 1.440 1.943
2.447
3.143 3.707
7
3.499
0.711 1.415 1.895 2.365
8 0.706 1.397 1.860
2.998
2.896 3.355
9 0.703 1.383 1.833
10 0.700 1.372 1.812
11 0.697 1.363 1.796 2.201 2.718 3.106
2.306
2.262 2.821 3.250
2.228 2.764 3.169
5
6
0.25
Transcribed Image Text:12 0.695 1.356 1.782 2.179
2.681
3.055
13 0.694 1.350
1.771
2.160 2.650
3.012
14
0.692 1.345
1.761 2.145 2.624
2.977
15
0.691 1.341 1.753
2.131
2.602
2.947
16
0.690 1.337 1.746
2.120
2.583
2.921
17
0.689
1.333 1.740 2.110 2.567
2.898
18
0.688 1.330 1.734 2.101
2.552
2.878
19
0.688 1.328 1.729
2.093
2.539 2.861
20
0.687
1.325 1.725
2.086
2.528
2.845
21
0.686
1.323 1.721
2.080
2.518
2.831
22
0.686
1.321
1.717
2.074
2.508
2.819
23
0.685
1.319 1.714 2.069
2.500
2.807
24
0.685 1.318 1.711
2.064
2.492
2.797
25 0.684 1.316 1.708
2.060
2.485
2.787
26
1.315 1.706
2.056
2.479
2.779
0.684
0.684 1.314
27
1.703 2.052
2.473
2.771
28 0.683 1.313 1.701
2.048 2.467
2.763
29 0.683 1.311 1.699
2.045
2.462
2.756
2.042 2.457
2.750
30
40 0.681 1.303
0.683 1.310 1.697
1.684
2.021
2.423
2.704
2.000 2.390
2.660
60 0.679 1.296 1.671
120 0.677 1.289 1.658
1.980
2.358 2.617
0.674 1.282 1.645 1.960 2.326 2.576
The critical t scores (the values that define the borders of the critical region) are
The estimated standard error is
The t statistic is
The t statistic
Therefore, the researcher
in the critical region. Therefore, the null hypothesis
rejected.
conclude that SAM-e has a significant effect on the moods of cancer patients.
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