MATH AP-A randomized comparative experiment examine

Subject: Mathematics    / Statistics
Question

A randomized comparative experiment examined whether a calcium supplement in the diet reduces the blood pressure of healthy men. The subjects received either a calcium supplement or a placebo for 12 weeks. The statistical analysis was quite complex, but one conclusion was that “the calcium group had lower seated systolic blood pressure (P = 0.008) compared with the placebo group.” Explain this conclusion, especially the P-value, as if you were speaking to a doctor who knows no statistics.

2. A new supplier offers a good price on a catalyst used in your production process. You compare the purity of this catalyst with that from your current supplier. The P-value for a test of “no difference” is 0.15. Can you be confident that the purity of the new product is the same as the purity of the product that you have been using? Explain.

3. More than 200,000 people worldwide take the GMAT examination each year as they apply for MBA programs. Their scores vary normally with mean about µ= 525 and standard deviation about = 100. One hundred students go through a rigorous training program designed to raise their GMAT scores. Test the hypotheses

: µ= 525
: µ > 525
in each of the following situations:

a) The students’ score is x = 541.4. Is this result significant at the 5% level?
b) The average score is x = 541.5. Is this result significant at the 5% level?
c) What conclusions may you draw by comparing the answers to parts a and b?

4.

A study examined the effect of exercise on how students perform on their final exam in statistics. The P-value was given as 0.87.

a) State null and alternative hypotheses that could have been used for this study.
b) Do you reject the null hypothesis?
c) What is your conclusion?
d) What other facts about the study would you like to know for a proper interpretation of the results?