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The following MINITAB output is for a two-way ANOVA.

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4SE Chapter 9

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4SE

The following MINITAB output is for a two-way ANOVA. Something went wrong with the printer, and some of the numbers weren’t printed.

Fill in the missing numbers in the table for (a) through (l). You may give ranges for the P-values.

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Vitamins  Organic: contain carbon  Micronutrients: essential in small amounts  Functions: promote and regulate body processes necessary for growth, reproduction, and the maintenance of health  Ex: making hemoglobin, helping harvest energy, assisting with immunity, promoting bone health, helping remove pollutants (oxidants) from the body NOTE: fat soluble vitamins are more likely to be toxic vs. water soluble vitamins because the body stores them while excess water soluble vitamins are excreted Vitamins Water soluble Fat soluble B Vitamins Vitamin C Vitamin A Thiamin Pantothenic acid Vitamin B Vitamin D Riboflavin 6 Vitamin E Niacin Folate Biotin Vitamin B 12 Vitamin K Vitamin Fortification  Adds nutrients to foods  Government mandated and voluntary  Prevents deficiencies leading to diseases but may also cause toxicity Tips for Preserving Vitamins Vitamin Bioavailability Affected by:  Absorption  Fat-soluble vitamins: need dietary fat  Transport in blood  Water-soluble vitamins: blood proteins  Fat-soluble vitamins: chylomicrons  Conversion of inactive provitamins or vitamin precursors into active vitamins Vitamin Absorption Coenzymes  Bind enzymes to promote their activity  Carriers of electrons, atoms, or chemical groups that participate in the reactions  Organic non-protein molecules  Ex: B vitamins NOTE: all B Vitamins are coenzymes, but not all coenzymes are B Vitamins Free Radicals & Antioxidants  Reactive oxygen molecules: cause oxidative damage by stealing electrons from other compounds, causing changes in their structure and function  Examples: Free radicals – generated by the body or from exposure to the environment  Antioxidants: destroy reactive oxygen molecules  Ex: Vitamin C, vitamin E, and selenium Meeting Vitamin Needs  DRIs include RDA, AI, and UL  Vitamin A and C (Iron,Calcium) amounts are required on food labels as %DV  This would change with proposed new food label: Vitamin A&C could be removed, while Vitamin D could be added Water-Soluble Vitamins  B vitamins: involved in converting the energy in carbohydrate, fat, and protein into ATP  Vitamin C: needed to make connective tissue and as an antioxidant  Choline: vitamin (will not be on our exam)  Not stored - need to be consumed regularly  Excreted in urine Thiamin (Vitamin B)  Coenzyme needed for glucose breakdown of glucose to provide energy  Needed for metabolism of other sugars, certain amino acids and synthesis of ribose (in RNA)  Important for nerve function because:  Glucose is nerve cell energy source  Needed for synthesis of neurotransmitters (chemical signals from neurons)  RDA: men = 1.2 mg/day; women = 1.1 mg/day  Sources: bran layer of whole grain, enriched grains, pork, legumes, and seeds  Deficiency:  Beriberi: weakness, nerve degeneration, heart changes  Wernicke-Korsakoff syndrome in alcoholics: mental confusion, psychosis, memory disturbances, coma  Excess: no reported effects Riboflavin Functions  Forms two active coenzymes that act as electron carriers functioning in reactions needed to produce ATP from carbohydrate, fat, and protein  Involved in converting folate, niacin, vitami6 B and vitamin K into their active forms.  RDA: men = 1.3 mg/day; women = 1.1 mg/day  Sources:  Animal: dairy products, liver, red meat, poultry, fish  Plant: whole grains, enriched grains, asparagus, broccoli, mushrooms, leafy greens  Deficiency:  injuries heal poorly  cracking of lips and corners of mouth  sensitivity to light  eye burning, tearing, itching  skin flaking around nose, eyebrows, earlobes  Excess: no reported effects but turns urine bright fluorescent yellow Niacin  Role: Coenzyme in glucose metabolism and synthesis of fatty acids and cholesterol  RDA: men = 16 mg NE/day ; women = 14 mg NE/day  Sources:  Animal: meats, fish  Plant: peanuts, whole and enriched grains, legumes, wheat bran, synthesized from the essential amino acid tryptophan  Deficiency:  Pellagra: fatigue, decreased appetite, indigestion, 4Ds = dermatitis, diarrhea, dementia, death  Excess: no reported effects from food but supplements can be toxic causing skin flushing and rash, tingling in hands and feet, nausea, vomiting, diarrhea, high blood sugar levels, liver function abnormalities, blurred vision Vitamin B6  Important for:  amino acid and protein metabolism  synthesis of nonessential amino acids, neurotransmitters (myelin sheath), hemoglobin  conversion of tryptophan into niacin  glycogen breakdown  3 forms: pyridoxal, pyridoxine, pyridoxamine  converted into active coenzyme pyridoxal phosphate needed for the activity of >100 enzymes in carbohydrate, fat, and protein metabolism  RDA: men and women ages 19 to 50 = 1.3 mg/day  Sources: chicken, fish, pork, organ meats, whole grains, legumes, sunflower seeds, bananas, broccoli, spinach, some fortified cereals (refined grains are not good sources)  Deficiency: poor growth, skin lesions, decreased immunity, anemia, neurological symptoms  Excess: no reported effects from food but supplements can be toxic causing severe nerve impairment Folate (folic acid) functions  Folate coenzymes needed for DNA synthesis (especially needed in rapidly-dividing tissues) and some amino acid metabolism  Important in early pregnancy for neural tube formation, which develops into the brain and spinal cord  Prevent homocysteine levels from rising to prevent heart disease NOTE: synthetic folate (folic acid) is absorbed better than natural folate; excess folate can mask a Vitamin B12 deficiency  RDA: men and women = 400 µg/day  Sources: enriched grains, leafy greens, asparagus, legumes, nuts, oranges, liver, yeast  Deficiency: neural tube defects including spina bifida and anencephaly, macrocytic or megaloblastic anemia, poor growth, nerve development and function problems, diarrhea, tongue inflammation, increased risk of heart disease and some cancers  Excess: concerns that excess will prevent folate deficiency symptoms and ma12 B deficiencies Vitamin B12 (cobalamin) functions Important for:  ATP production from certain fatty acids  Conversion of homocysteine to methionine  Maintenance of myelin coating on nerves  Amino acid and protein metabolism  RDA: men and women = 2.4 µg/day  Sources: found naturally only in animal products, also in fortified products  Deficiency: pernicious anemia, increased homocysteine, decreased folate activation, numbness and tingling, gait abnormalities, memory loss, disorientation, paralysis, death  Excess: no reported effects from intakes of up to 100 µg/day from food or supplements Folate & Vitamin B12  Needed for synthesis of neurotransmitters, hormones, bile acids, and carnitine (needed for fatty acid breakdown)  Antioxidant in blood and body fluids  Helps maintain the immune system  Regenerates active antioxidant form of vitamin E  Enhances iron absorption Vitamin C (ascorbic acid)  Synthesis and maintenance of collagen, the base of all connective tissue  Needed for synthesis of neurotransmitters, hormones, bile acids, and carnitine (needed for fatty acid breakdown)  Antioxidant in blood and body fluids Helps maintain the immune system Regenerates active antioxidant form of vitamin E Enhances iron absorption  RDA: men = 90 mg/day, women = 75 mg/day  Sources: citrus fruits, strawberries, kiwis, cantaloupe, cabbage-family and dark-green vegetables, green and red peppers, okra, tomatoes, potatoes  Deficiency: scurvy (gum and tooth problems, joint pain, bleeding, poor wound healing, bone fractures, fatigue, depression, hysteria)  Excess: excessive vitamin C supplementation can cause diarrhea, nausea, abdominal cramps, possible increased kidney stone formation Water-soluble Vitamins  B vitamins: involved in converting the energy in carbohydrate, fat, and protein into ATP  Vitamin C: needed to make connective tissue and as an antioxidant  Choline: vitamin  Not stored - need to be consumed regularly  Excreted in urine Fat-soluble Vitamins  Vitamins A, D, E, & K  Found with fats in foods  Require special handling for absorption, transport and excretion  Excretion limitations increases the risk of toxicity  Stored in the liver and fatty tissues  Intakes can vary without a risk of deficiency if average intake over weeks/months meets needs Vitamin A  Retinoidschemical forms of preformed vitamin A  Retinol, retinal, retinoic acid  Carotenoids: yellow-orange pigments synthesized by plants and many microorganisms  Some are vitamin A precursors converted to retinoids  Example: beta-carotene, provitamin converted into vitamin A  Cell differentiation  Immature cells change in structure and function to become specialized by changing gene expression (turning genes on and off)  Necessary for maintenance of epithelial tissue  Part of rhodopsin, a visual pigment in the eye  When light strikes rhodopsin, it initiates a series of events that result in a nerve signal being sent to the brain, which allows us to see  Carotenoids may function as antioxidants  RDA: men = 900 µg/day, women = 700 µg/day  Sources: vitamin A in animal products (eggs, dairy), provitamin A in fruits and vegetables, beta-carotene in orange, yellow, and dark green vegetables  Deficiency: xerophthalmia (night blindness progressing to permanent blindness), abnormal jaw bone growth in children, increased infections  Excess: nausea, vomiting, headache, dizziness, blurred vision, lack of muscle coordination, birth defects, liver damage, bone fractures; excess carotene can cause hypercarotenemia Vitamin D  Made in skin with exposure to ultraviolet (UV) light  Inactive until modified in liver and kidneys  Essential in the diet only when exposure to sunlight is limited or the body’s ability to synthesize it is reduced Vitamin D Activation Vitamin D Functions  Maintains normal levels of the minerals calcium and phosphorus in the blood  Calcium is needed for bone health and functioning of nerves, muscles, glands, and other tissues  Low blood calcium stimulates parathyroid hormone (PTH) release which stimulates vitamin D activation  Changes gene expression  Intestines: turns on genes for calcium absorption  Bone: turns on genes bone breakdown  RDA: adults 70 and under = 600 IU (15g)/ day  Sources: not widespread in diet, liver, egg yolks, oily fish (for example, salmon), fortified foods  Deficiency: low calcium absorption leading to rickets in children (pigeon breast and bowed legs) and osteomalacia, which can lead to osteoporosis in adults Excess: causes high calcium concentrations in blood and urine, deposition of calcium in soft tissues such as the blood vessels and kidneys, and cardiovascular damage Barriers to Meeting Vitamin D Needs  Age  Geographical Location  Use of sunscreen/ cultural body coverings: block skin’s exposure to the sun  Skin color: the amount of melanin in your skin can bock some UV rays Vitamin E  Antioxidant  Protects lipids including those in membranes of red blood cells, white blood cells, nerve cells, lung cells  Defends cells against damage caused by heavy metals (lead and mercury)  Reduced risk of heart disease, cancer, Alzheimer’s disease, macular degeneration, other chronic diseases  Possible anti-inflammatory functions, modulation of immunity, regulation of cell growth and death genes, detoxification of harmful substances  RDA: adults = 15 mg alpha-tocopherol/day  Sources: seeds, nuts, plant oils, leafy-green vegetables, wheat germ, fortified cereals  Deficiency: hemolytic anemia in infants; rare in adults causing poor muscle coordination, weakness, impaired vision  Excess: no reported effects from food but large doses can interfere with blood clotting Vitamin K Functions  Needed for:  production of clotting factors  synthesis of proteins involved in bone formation and breakdown ANTICOAGULANT S Supplements  Contain vitamins and minerals, herbs and other plant-derived substances, and/or body compounds not essential in the diet  Help obtain adequate amounts of specific nutrients but do not provide all the benefits of foods Herbal Supplements  Herb: nonwoody, seed-producing plant that dies at the end of the growing season  Also refers to any botanical or plant-derived substance  Ex: garlic, ginko, saw palmetto, St. John’s wort Regulation of Supplements  Dietary Supplement Health and Education Act (DSHEA) of 1994 defined the term dietary supplement and created labeling standards  FDA established “current Good Manufacturing Practice” (cGMP) regulations Requires manufacturers to test their products to ensure identity, purity, strength, and composition  FDA pre-market review required if ingredient not sold in the US before October 15, 1994 Choosing Supplements  Do not exceed 100% of Daily Values  Consider why you want it  Compare product costs  Read the label  Check the expiration date  Consider your medical history  Approach herbal supplements with caution  Report harmful effects What Should you do  Focus on foliage for folate, vitamin A, and vitamin K  B (vitamin) sure  Get your antioxidants  Try for 5 colors of fruits and veggies each day  Soak up some D  Get outside to stay fit and make some vitamin  Have three servings of dairy per day boost intake

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Chapter 9, Problem 4SE is Solved
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Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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The following MINITAB output is for a two-way ANOVA.