Question

A researcher wishes to determine if the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10-week period of time. After this course of treatment, each subject has his or her memory tested using a standard memory test. Suppose the scores on this test of memory for all potential subjects taking the herbal extract follow a Normal distribution with mean ? and standard deviation ? = 6. Suppose also, that in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation ? = 4. The researcher, therefore, decides to test the hypotheses H0: ? = 50, Ha: ? > 50 To do so, the researcher has 100 subjects follow the protocol described above. The mean score for these students is = 55.2 and the P-value is less than 0.0001. Reference: Ref 16-1 Suppose that another researcher attempts to replicate the study described above. She uses a sample of 10 subjects and observes a sample mean memory score of 55.2, the same as the sample mean described in the first study. It is appropriate to conclude which of the following?

A. She has obtained the same sample mean as the first researcher, so her P-value will be the same as that of the first researcher.

B. She has obtained the same sample mean as the first researcher, but her P-value will be smaller than that of the first researcher.

C. She has obtained the same sample mean as the first researcher, but her P-value will be greater than that of the first researcher.

D. None of the above

Answer 1

Answer:

C. She has obtained the same sample mean as the first researcher, but her P-value will be greater than that of the first researcher.

Step-by-step explanation:

• the hypotheses are H0: = 50, Ha: > 50

• With 100 samples, mean=55.2 and the P-value is less than 0.0001
• with 10 samples , mean=55.2 and P-value=?

test statistic can be found using the equation

$\frac{X-M}{\frac{s}{\sqrt{N} } }$ where

• X = 55.2

• M =50

• s is the standard deviation

• N is the sample size

Thus, as the sample size gets smaller, test statistics gets smaller.  

Therefore, P-value is greater.