Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, and Nyberg, 2004). In a typical study, a researcher obtains a sample of n=16 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test form a normal distribution with a mean of

μ=50 and a standard deviation of s.d=12 . The sample of research participants had an average of M=54 .

a)Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined.

b)Using the standard 4-step procedure, conduct a two-tailed hypothesis test with alpha=.05 to evaluate the effect of the supplements.

What "two variables"? I only see the memory test.

Z = (score-mean)/SEm

SEm = SD/√n

Look in the back of your statistics textbook for a table called something like “area under normal distribution” to find the proportion/probability related to the Z score.

a) The null hypothesis for this study would be: There is no effect of taking herbal supplements (Ginkgo biloba and Ginseng) on memory and learning in healthy adults.

b) To conduct a two-tailed hypothesis test, we can follow the standard 4-step procedure:

Step 1: State the hypotheses:
- Null hypothesis: The mean memory test score for participants taking herbal supplements is equal to the mean memory test score for the general population (μ = 50).
- Alternative hypothesis: The mean memory test score for participants taking herbal supplements is not equal to the mean memory test score for the general population (μ ≠ 50).

Step 2: Set the criteria for decision-making:
Since the significance level (alpha) is given as .05 and it's a two-tailed test, we divide the alpha by 2, resulting in .025. This means we will reject the null hypothesis if the p-value is less than .025.

Step 3: Compute the test statistic:
We need to use the z-test since the population standard deviation is known. To calculate the z-score, we use the formula:
z = (M - μ) / (s / sqrt(n))

Given:
M (sample mean) = 54
μ (population mean) = 50
s (standard deviation) = 12
n (sample size) = 16

Plugging in the values:
z = (54 - 50) / (12 / sqrt(16))
z = 4 / (12 / 4)
z = 1

Step 4: Make a decision:
Since it is a two-tailed test, we compare the absolute value of the z-score to the critical values for alpha/2 (0.025). When the absolute value of the z-score is greater than the critical value, we reject the null hypothesis.

From the z-table, the critical z-value for alpha/2 (0.025) is approximately 1.96.

Since the calculated z-score (1) is not greater than the critical value (1.96), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that the herbal supplements have a statistically significant effect on memory and learning in healthy adults.