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 = 24.4 with a standard deviation of s = 6.02. In the general population of HIV patients, the standardized test is known to have a population mean of μ = 27.2. 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:
H₀: μSAM-eSAM-e = 27.2; H₁: μSAM-eSAM-e ≠ 27.2
H₀: μSAM-eSAM-e ≤ 27.2; H₁: μSAM-eSAM-e > 27.2
H₀: MSAM-eSAM-e ≥ 27.2; H₁: MSAM-eSAM-e > 27.2
H₀: MSAM-eSAM-e ≥ 27.2; H₁: MSAM-eSAM-e < 27.2
Assume that the depression scores among patients taking SAM-e are normally distributed. You will first need to determine the degrees of freedom. There are19 degrees of freedom.
Use the t distribution table to find the critical region for α = 0.01.
The t Distribution:
df |
Proportion in One Tail |
|||||
---|---|---|---|---|---|---|
0.25 |
0.10 |
0.05 |
0.025 |
0.01 |
0.005 |
|
Proportion in Two Tails Combined |
||||||
0.50 |
0.20 |
0.10 |
0.05 |
0.02 |
0.01 |
|
1 | 1.000 | 3.078 | 6.314 | 12.706 | 31.821 | 63.657 |
2 | 0.816 | 1.886 | 2.920 | 4.303 | 6.965 | 9.925 |
3 | 0.765 | 1.638 | 2.353 | 3.182 | 4.541 | 5.841 |
4 | 0.741 | 1.533 | 2.132 | 2.776 | 3.747 | 4.604 |
5 | 0.727 | 1.476 | 2.015 | 2.571 | 3.365 | 4.032 |
6 | 0.718 | 1.440 | 1.943 | 2.447 | 3.143 | 3.707 |
7 | 0.711 | 1.415 | 1.895 | 2.365 | 2.998 | 3.499 |
8 | 0.706 | 1.397 | 1.860 | 2.306 | 2.896 | 3.355 |
9 | 0.703 | 1.383 | 1.833 | 2.262 | 2.821 | 3.250 |
10 | 0.700 | 1.372 | 1.812 | 2.228 | 2.764 | 3.169 |
11 | 0.697 | 1.363 | 1.796 | 2.201 | 2.718 | 3.106 |
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 | 0.684 | 1.315 | 1.706 | 2.056 | 2.479 | 2.779 |
27 | 0.684 | 1.314 | 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 |
30 | 0.683 | 1.310 | 1.697 | 2.042 | 2.457 | 2.750 |
40 | 0.681 | 1.303 | 1.684 | 2.021 | 2.423 | 2.704 |
60 | 0.679 | 1.296 | 1.671 | 2.000 | 2.390 | 2.660 |
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 in the critical region. Therefore, the null hypothesis rejected.
Therefore, the researcher conclude that SAM-e has a significant effect on the moods of HIV patients.
S-adenosyl methionine (SAM-e) is a naturally occurring compound in human cells that is thought to have...
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