Problem 1. (10 pts.) Calcium is an essential mineral that regulates the heart, is important for blood clotting and for building healthy bones. The National Osteoporosis Foundation recommends a daily calcium intake of 1000-1200 mg/day for adult men and women. While calcium is contained in some foods, most adults do not get enough calcium in their diets and take supplements. Unfortunately some of the supplements have side effects such as gastric distress, making them difficult for some patients to take on a regular basis.

A study is designed to test whether there is a difference in mean daily calcium intake in adults with normal bone density, adults with osteopenia (a low bone density which may lead to osteoporosis) and adults with osteoporosis. Adults 60 years of age with normal bone density, osteopenia and osteoporosis are selected at random from hospital records and invited to participate in the study. Each participant's daily calcium intake is measured based on reported food intake and supplements. Using the data and the Excel ANOVA output (using a level of significant ? = 0.10 on the second page, answer the following questions.

1. What is the total number of participants in the study?
2. What is the average bone density for all of the participants?
3. What is the average bone density for participants with normal bone density?
4. Determine each of the following values
5. SSE
6. MST
7. Total Variation
8. Using the summary data in the Excel output, confirm the value of the F statistic
9. Using the F statistic, what conclusion do you make?
10. Using the p-value, what conclusion do you make?
11. What is the critical F value if we change the level of significance to 0.05?

Homework 11. Normal Bone Density Osteopenia Osteoporosis 1024 864 767 851 936 559 837 600 948 768 684 766 647 134 344 682 599 308 837 599 940 775 686 778 640 434 341 686 598 298 Anova: Single Factor SUMMARY Groups Count Sum Average Variance Column 1 10 7747 774.7 14076.90 Column 2 10 6434 643.4 25925.16 Column 3 10 6049 604.9 70484.32 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 158513.3 2.0000 79256.63 2.1520 0.1358 2.5106 Within Group 994377.4 27.0000 36828.79 Total 1152890.7 29.0000