Question

- Une, alls page may not function correctly. Click here to learn more. mm 5. Two-tailed hypothesis testing - Step by step Aa 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-cholce self-report inventory for measuring the severity of depression RUS NE The scores from the sample produced a mean of M = 27.9 with 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: O Ho: SAM- S 30.3; H1: USAM-- > 30.3 Ho: PSAM-2 30.3; H1: PSA-e < 30.3 O Ho: PSAM- - 30.3; Hy: PSAM-- + 30.3 O Ho: MSAM- 30.3; H: MSAM > 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 distribution table to find the critical region form .05.

Answer 1

Question 5

Null Hypothesis : H₀ : $\mu _$_SAM-e  = 30.3

Alternative Hypothesis : H_a : $\mu _$_SAM-e $\neq$ 30.3

sample standard deviation = s = 3.20

sample mean = $\bar x$ = 27.9

Here sample size = n = 20

degree of freedom = n -1 = 20 - 1 = 19

The critical t - scores for $\alpha$ = 0.05

t_critical = 2.093

stanadard error = se = s/sqrt(n) = 3.20/sqrt(20) = 0.7155

t statistic is

t = (27.9 - 30.3)/0.7155 = -3.3541

Here the t statistic is in critical region. Therefore, null hypothesis shall be rejected.

Therefore, the researcher would be able to conclude that SAM-e has a significant effect on the moods of HIV patients.