A researcher wishes to determine if the use of an herbal extract improves memory

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

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

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

None of the above

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.

Explanation / Answer

here, x = 55.2 , mean = 50 , s = 4 , n = 10

z = ( x - mean) / (s / sqrt(n))

= ( 55.2 - 50 ) / (4 / sqrt(10))

= 4.11

Now, we need to find p value using z = 4.11 for alpha = 0.05

P value = 0.00002

As we calculated above we got the conclusion are as;

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

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