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 mu and standard deviation alpha = 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 alpha = 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 alpha = 4. The researcher, therefore, decides to test the hypotheses H_0: mu = 50, H_a: mu > 50 To do so, the researcher has 100 subjects follow the protocol described above. The mean score for these students is r = 55.2 and the F-value is less than 0.0001. Which statement is an appropriate to conclusion? The researcher has conclusively proved that use of this herbal extract improves memory. The researcher has strong evidence that people that use this herbal extract, on average, have higher memory test scores than those that don't use this extract. However, the difference may or may not be important. The researcher has strong evidence that use of this herbal supplement improves memory, and because the P-value is so small, the difference must be substantial. None of the above A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of r = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean mu. The P-value for the one-sample t test is: larger than 0.10. between 0.10 and 0.05. between 0.01 and 0.05. below 0.01. To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times, and the mean r of the weights is computed. Suppose the scale readings are Normally distributed, with unknown mean mu and standard deviation = 0.01 g. How large should n be so that a 95% confidence interval for mu has a margin of error of 0.0001? 100

Explanation / Answer

Part 1

Since the mean is 55.2>50,

& also the p-value (0.0001) is less than 0.05(for 95% confidence), we reject the null hypothesis.

We can say with, 99.99% confidence, that the use of this supplement improves memory test sscores. However, the difference may or may not be important.

Correct answer is optionB

Part 2

Correct answer is option B (between 0.10 & 0.05)

The two-tailed P value equals 0.0891
By conventional criteria, this difference is considered to be not quite statistically significant.

Confidence interval:
The hypothetical mean is 150.00
The actual mean is 143.00
The difference between these two values is -7.00
The 95% confidence interval of this difference:
From -15.14 to 1.14

Intermediate values used in calculations:
  t = 1.7638
  df = 27
  standard error of difference = 3.969

Part 3 : Not enough data.

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