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Applet Exercise Refer to Exercise 9.13. Scroll down to the

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 14E Chapter 9

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 14E

Problem 14E

Applet Exercise Refer to Exercise 9.13. Scroll down to the portion of the applet labeled “Mean of Normal Data.” Successive observed values of a standard normal random variable can be generated and used to compute the value of the sample mean . These successive values are then plotted versus the respective sample size to obtain one “sample path.”

a Do you expect the values of  to cluster around any particular value? What value?

b If the results of 50 sample paths are plotted, how do you expect the variability of the estimates to change as a function of sample size?

c Click the button “New Sequence” several times. Did you observe what you expected based on your answers to parts (a) and (b)?

Reference

Applet Exercise Refer to Exercises 9.9–9.12. Access the applet Point Estimation.

a Chose a value for p. Click the button “New Sequence” repeatedly. What do you observe?

b Scroll down to the portion of the applet labeled “More Trials.” Choose a value for p and click the button “New Sequence” repeatedly. You will obtain up to 50 sequences, each based on 1000 trials. How does the variability among the estimates change as a function of the sample size? How is this manifested in the display that you obtained?

Reference

Applet Exercise Refer to Exercise 9.11. What happens if each sequence is longer? Scroll down to the portion of the screen labeled “Longer Sequences of Trials.”

a Repeat the instructions in parts (a)–(c) of Exercise 9.11.

b What do you expect to happen if p is not 0.5? Use the button in the lower right corner to change to value of p. Generate several sequences of trials. Comment.

Reference

Applet Exercise Refer to Exercises 9.9 and 9.10. How can the results of several sequences of Bernoulli trials be simultaneously plotted? Access the applet PointbyPoint. Scroll down until you can view all six buttons under the top graph.

a Do not change the value of p from the preset value p = .5. Click the button “One Trial” a few times to verify that you are obtaining a result similar to those obtained in Exercise 9.9. Click the button “5 Trials” until you have generated a total of 50 trials. What is the value of  that you obtained at the end of this first sequence of 50 trials?

b Click the button “New Sequence.” The color of your initial graph changes from red to green. Click the button “5 Trials” a few times. What do you observe? Is the graph the same as the one you observed in part (a)? In what sense is it similar?

c Click the button “New Sequence.” Generate a new sequence of 50 trials. Repeat until you have generated five sequences. Are the paths generated by the five sequences identical? In what sense are they similar?

Reference

Applet Exercise Refer to Exercise 9.9. Scroll down to the portion of the screen labeled “Try different probabilities.” Use the button labeled “p =” in the lower right corner of the display to change the value of p to a value other than .5.

a Click the button “One Trial” a few times. What do you observe?

b Click the button “100 Trials” a few times. What do you observe about the values of  as the number of trials gets larger?

Reference

Applet Exercise How was Figure 9.1 obtained? Access the applet PointSingle at academic. cengage.com/statistics/wackerly. The top applet will generate a sequence of Bernoulli trials

times. How many trials n have you simulated? What value of  did you observe? Is the value close to .5, the true value of p? Is the graph a flat horizontal line? Why or why not?

c Click the button “100 Trials” a single time. What do you observe? Click the button “100 Trials” repeatedly until the total number of trials is 1000. Is the graph that you obtained identical to the one given in Figure 9.1? In what sense is it similar to the graph in Figure 9.1?

d Based on the sample of size 1000,what is the value of ? Is this value what you expected to observe?

e Click the button “Reset.” Click the button “100 Trials” ten times to generate another sequence of values for  .Comment.

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Study Guide for Exam 1 FCFN 340 1. What is the most important factor that influences food choice a. Taste is the most important factor in food selection. 2. Know and understand the differing ways that people make food choices. a. Taste and enjoyment b. Culture and environment i. Living environment  Availability and accessibility ii. Food environment  Size and shape of plates and glassware  Packaging of foods  Lighting c. Social life and trends i. Group size  Individuals eat more food when eating with others.  Meal size increases by over 40 percent.  More food is eaten as the group size increases. ii. Activities  Food intake increases when eaten during an activity.  Example: Patrons are more likely to eat popcorn at a movie theater when they are with friends. iii. Popular food trends d. Nutrition knowledge i. Perception of foods as healthy or unhealthy  Example: Avoid high-sodium foods to reduce blood pressure. ii. Current state of health affects food choices.  Example: Avoid foods associated with weight gain or loss. e. Advertising i. Advertising influences food selection, especially for children and adolescents.  Manufacturers spend $10 billion to $15 billion annually on food advertising.  The most advertising dollars are spent on breakfast cereals, candy, gum, and carbonated soft drinks.  Advertising for fruits and vegetables is rare. f. Time, convenience, and cost i. Time and convenience are factors for those with busy schedules.  Average time spent preparing a meal (including cleanup) is less than 30 minutes.  Supermarkets are providing prepared foods and partially prepared foods.  People eat out more today than they did a few decades ago. ii. Cost  Fast foods are often cheaper or perceived as cheaper than nutritious foods and are selected more often.  Large Fries at McDonalds = $1.79  Bag of White Potatoes = $3.00 (av. 10-12 potatoes)  Excess fast food consumption increases risk for obesity.  Individuals purchase nutritious foods when offered at lower prices. g. Habits and emotions i. Daily routine and habits affect when and what you eat. ii. Emotions can sometimes drive food choices. 3. What are phytochemicals Zoochemicals a. Phytochemicals- nonnutritive plant chemicals found in foods that reduce risk for developing chronic diseases i. In foods, 900 different phytochemicals ii. Work with other nutrients in foods to offer disease-fighting characteristics b. Zoochemicals- nonnutritive animal compounds that play a role in fighting chronic diseases i. Example: Omega-3 fatty acids from fish may improve heart health and reduce inflammation. 4. What are the macronutrients Micronutrients Which one is most abundant a. Macronutrients- nutrients the body needs in large amounts i. Carbohydrates, fats (lipids), protein, and water ii. Macro are most abundant, specifically water b. Micronutrients- essential nutrients the body needs in smaller amounts i. Vitamins and minerals 5. Which nutrients are organic Inorganic a. Nutrients that contain carbon in their chemical structures are "organic." b. Organic nutrients include: i. Carbohydrates ii. Proteins iii. Lipids iv. Vitamins c. Inorganic nutrients include: i. Minerals ii. Water 6. Know how to figure calorie content (refer to the calculation slides in Chapter 1 ppt). a. Energy-yielding nutrients i. Carbohydrate = 4 kcal/gram ii. Protein = 4 kcal/gram iii. Fat (lipid) = 9 kcal/gram b. Alcohol, a nonnutrient, also provides kilocalories. i. Alcohol = 7 kcal/gram c. d. 7. The consumption of excess calories leads to the accumulation of what, within the body a. Unused energy is stored predominantly as fat. b. Using more energy than is consumed results in fat breakdown. 8. Know the ABCDs of nutrition assessment (anthropometric, biochemical, etc.) and be able to choose examples of each. a. b. Anthropometric data measures body size or body composition. c. Biochemical data laboratory tests assess nutritional status by measuring the nutrient levels in body fluids, including blood and urine. i. Might measure:  How fast a nutrient is excreted through urine  Metabolic by-products of various nutrients in urine 9. For what purpose was the NHANES established a. National surveys have been developed by federal agencies to assess the health and nutritional status of Americans. b. The National Health and Nutrition Examination Survey (NHANES) i. Series of surveys that evaluate the nutritional status of Americans of all ages 10. How would you describe the current typical American diet a. Poor dietary practices may be due to where Americans eat. i. Most Americans eat in the car, buy prepared meals, or eat in front of the TV or computer. b. Excess intake i. Added sugar ii. 16 percent of daily total kcal intake iii. Sodium iv. Saturated fat c. Too little intake i. Fiber ii. Some vitamins (vitamin D) iii. Some minerals (potassium and calcium) iv. Most men meet the recommendations for vitamins and minerals. v. Women tend to be low in iron. d. More than 35 percent of adults are obese. i. Leads to higher rates of:  Type 2 diabetes  Heart disease  Cancer  Stroke 11. Be familiar with the chart that tells what elements are found in each nutrient (i.e. carbon, hydrogen, etc.) . a. 12. What does the BMI measure a. Body mass index (BMI) is a measure of body fat based on height and weight that applies to adult men and women. b. BMI measures the mass of the body in relation to height and weight. i. And by taking this calculation one can make a relatively accurate assumption of body fat percentage. ii. Whether your current weight in relation to your height is considered underweight, normal, overweight or obese. 13. Understand the differing types of malnutrition. a. Undernutrition: A person's nutrient and/or energy needs aren't met through diet b. Overnutrition: Excess nutrients and/or energy are consumed c. Malnutrition: The long-term consequence of consuming too many or too little nutrients or energy 14. Know energy density, nutrient density, and the differences between the two. Spend some time with these slides/sections in the text. a. See part b on #15 15. Know the key principles of healthy eating. a. Healthy eating means an individual's diet incorporates: i. Balance  A balanced diet includes a healthy proportion of nutrients to maintain health and prevent disease. ii. Variety  Variety is the dietary principle of including a mixture of different food groups and foods within each group.  Eating a variety of foods improves diet quality.  No food or food group contains every single nutrient needed to be healthy. iii. Moderation  Moderation is the dietary principle of consuming reasonable but not excessive amounts of foods and nutrients.  All foods—healthy or unhealthy—can be included in a healthy diet as long as they are consumed in moderation.  Consume foods high in added sugars and fat in smaller amounts.  Limit portions and number of servings of nutrient-dense and energy-dense foods such as nuts. b. Additional principles include: i. Nutrient density  Nutrient density is the measurement of the nutrients in a food compared to the kilocalorie content.  High in nutrients and low in kilocalories  Provide more nutrients per kilocalorie  Low in fat and added sugar  Some nutrient-dense foods are high in kilocalories (e.g., avocado, peanut butter).  Be mindful of the kilocalories in these foods and consume them in moderation. ii. Energy density  Energy density is a measurement of the kilocalories in a food compared with the weight of the food.  Most high-fat foods are energy dense.  High energy dense foods: Foods high in energy and low in volume or weight.  Low-energy-dense foods  Eating low-energy-dense foods can promote weight loss.  Eating low-energy-dense foods means eating larger portions for the same number of kilocalories, which may improve satiety and decrease hunger. 16. What is EER based upon a. Estimated Energy Requirement (EER) i. Amount of daily energy needed to maintain a healthy body weight and meet energy needs based on age, gender, height, weight, and activity level ii. No DRI has been set for energy intake. iii. Individuals who consume more energy than needed will gain weight. 17. Which government agency sponsors ChooseMyPlate.gov a. The USDA i. Dietary guidelines updated every 5 years by the U.S. Department of Agriculture (USDA) and the Department of Health and Human Services (DHHS) b. Food guidance systems are graphics used to summarize guidelines to healthy eating. c. MyPlate is a visual depiction of the recommendations in the Dietary Guidelines for Americans, 2010. d. ChooseMyPlate.gov is a web-based tool that provides: i. Information, tips, and tools to help people build a healthier diet ii. An interactive food guidance system that provides personalized food plans 18. What items must be included on a food label a. Every packaged food must be labeled with: i. Name of food ii. Net weight—the weight of the food in the package, excluding weight of the package or packing material iii. Name and address of the manufacturer or distributor iv. List of ingredients in descending order by weight b. Nutrition Labeling and Education Act in 1990 mandated: i. Uniform nutritional information ii. Serving sizes iii. Specific criteria for nutrient descriptors and health claims c. Additional requirements for the label since 1990 include: i. Nutrition information: total kilocalories, kilocalories from fat, total fat, saturated fat, trans fats, cholesterol, sodium, total carbohydrate, dietary fiber, sugars, vitamin A, vitamin C, calcium, and iron ii. Uniform serving sizes among similar products iii. Indication of how a serving of the food fits into an overall daily diet iv. Uniform definitions for descriptive label terms such as "light" and "fat free" v. Health claims that are accurate and science-based, if made about the food or one of its nutrients vi. Presence of the eight common allergens  Some foods are under the FDAs voluntary point-of-purchase program.  Raw fruits and vegetables and fresh fish do not have a label.  Stores must post the nutrition information on the most commonly eaten fruits, vegetables, and fish near where the products are sold.  Meat and poultry is regulated by the USDA.  Food labels in grocery stores are required and must indicate in which country the animal was born, raised, and slaughtered. d. Rules about nutrients i. Nutrients added to the product must be listed. ii. Nutrients associated with a health claim must be listed. iii. Serving size must be listed both by weight in grams and common household measures. iv. The rest of the information on the panel is based on the listed serving size.  Some foods are exempt from having a Nutrition Facts panel.  Plain coffee and tea  Some spices, flavorings, and other foods that offer negligible amounts of nutrients  Ready-to-eat foods that are prepared and sold in retail establishments and restaurants  Food produced by small businesses 19. Know some of the good ways to limit intake/control portion sizes. a. Balance kilocalories. i. Enjoy your food, but eat less. ii. Avoid oversized portions. b. Increase the following foods. i. Make half your plate fruits and vegetables. ii. Make at least half your grains whole grains. iii. Switch to fat-free milk or low-fat (1%) milk. c. Reduce the following foods. i. Compare sodium in foods like soup, bread, and frozen meals—and choose the foods with lower numbers. ii. Drink water instead of sugary drinks. d. The takeaway message i. Balance kilocalories daily and choose nutrient-dense foods from each food group. ii. Choosing nutrient-dense foods lowers fat and sugar in the diet. iii. Being physically active helps with weight management and reducing risk for disease. 20. What are the events that allow nutrients from foods to be used by the body a. Digestion: The process of breaking down food into individual molecules small enough to be absorbed through the intestinal wall b. Absorption: The process of moving nutrients from the gastrointestinal (GI) tract into the circulatory system c. Transport: The process of moving absorbed nutrients throughout the body through the circulatory and lymph systems d. Elimination: The excretion of undigested and unabsorbed food through the feces 21. Know the major organs involved in digestion and their functions (what occurs in each). a. See the Actions column i. ii. b. Digestion Organs i. Mouth  Once food has been adequately chewed and moistened, the tongue rolls it into a bolus and it enters the pharynx to be swallowed.  After the food leaves the mouth, it enters the esophagus.  Saliva  Dissolves small food particles  Contains the enzyme amylase, which begins to break down carbohydrate  In adults, no other chemical digestion takes place in the mouth. ii. Esophagus  The esophagus transports food and fluids to the stomach.  There are two sphincters in the esophagus:  Upper esophageal sphincter: Allows the bolus of food to enter the esophagus  Lower esophageal sphincter (LES): Allows the bolus of food to enter the stomach iii. Stomach  The stomach mixes food with various gastric juices to chemically break it down into smaller pieces.  Mechanical digestion occurs in the stomach as the muscles of the stomach mix, churn, and push the contents with gastric juices.  When empty the stomach holds 1 cup; it can expand to hold up to 1 gallon.  Chyme is the semiliquid, partially digested food mass that leaves the stomach and enters the small intestine.  Approximately 1 tsp of chyme leaves the stomach and enters the small intestine every 30 seconds.  The pyloric sphincter is the gateway for chyme to enter the small intestine from the stomach. iv. Small Intestine  Most digestion occurs in small intestine  The small intestine consists of three segments.  Duodenum: 10 inches long  Jejunum: 8 feet long  Ileum: 12 feet long  Mechanical and chemical digestion take place in the small intestine.  Muscular contractions push chyme forward; digestive secretions break down nutrients.  The surface of the small intestine is lined with villi, which help maximize absorption.  The contact time in the small intestine is 3 to 10 hours, depending on the food eaten. v. Large Intestine  Large Intestine absorbs water and some nutrients  Chyme enters the large intestine through the ileocecal valve.  The large intestine is 5 feet long and 2.5 inches in diameter.  The large intestine has three segments.  Cecum: The beginning of the intestine  Colon: The largest part of the intestine  Rectum: Final 8-inch portion of the large intestine  It is the site of water, sodium, potassium, and chloride absorption.  Bacteria produce vitamin K, thiamin, riboflavin, biotin, and vitamin B 12but only biotin and vitamin K can be absorbed.  Bacteria in the colon ferment some undigested and unabsorbed carbohydrates into simpler compounds, methane gas, carbon dioxide, and hydrogen.  Fermented fiber produces short-chain fatty acids.  In the large intestine, 1 liter of fluid material is gradually reduced to 200 grams of brown fecal material.  The intestinal matter passes through the large intestine in 12 to 70 hours, depending on the person's health, age, diet, and fiber intake.  Stool is propelled through the large intestine until it reaches the rectum, the 8-inch portion of the large intestine.  The anus is the opening of the rectum, or end of the GI tract.  The final stage of defecation is under voluntary control.  It is also influenced by age, diet, prescription medications, health, and abdominal muscle tone. c. Accessory Organs of Digestion i. Salivary glands  Dissolve small food particles to ease the process of swallowing food  The body produces 1 quart of saliva per day.  Saliva contains water, mucus, electrolytes, and a few enzymes. ii. Liver  It is the largest organ in the body, weighing 3 pounds.  It is a major player in the digestion, absorption, and transport of nutrients.  It is essential in carbohydrate metabolism.  It makes proteins.  It manufactures bile salts that are used to digest fats.  It is the site of alcohol metabolism and removes and degrades toxins and excess hormones. iii. Gallbladder  Receives bile from the liver via common hepatic duct  Concentrates bile  Releases bile into small intestine via common bile duct iv. Pancreas  Endocrine function: Releases hormones to maintain blood glucose levels  Exocrine function: Secretes digestive enzymes into the small intestine d. 22. How do nutrients travel to the rest of the body a. Nutrients are absorbed into the bloodstream or lymphatic system. i. Water-soluble nutrients are absorbed into the cardiovascular system through the hepatic portal vein to the liver. ii. Carbohydrates, amino acids, and water-soluble vitamins b. Fat-soluble nutrients are absorbed into the lymphatic system. i. Fat-soluble vitamins, long-chain fatty acids, and proteins are too large to be transported via the capillaries. c. The waste products that remain after nutrient absorption are removed by the excretory system. d. The kidneys filter the blood, allowing waste products to be concentrated in the urine and excreted. e. 23. How do you treat/avoid constipation a. Constipation: Infrequent passage of dry, hardened stools i. Often due to insufficient fiber or water intake ii. Other causes include stress, inactivity, smoking cessation and various illnesses. iii. Treatment  Exercise, normal eating patterns, and proper rest can help resolve constipation.  Laxatives should be used sparingly, as they can cause dehydration, salt imbalances, and laxative dependency. iv. Avoid colon cleansing (enema) as a treatment.

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Chapter 9, Problem 14E is Solved
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Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

Since the solution to 14E from 9 chapter was answered, more than 270 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This full solution covers the following key subjects: trials, button, click, applet, exercise. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. The answer to “Applet Exercise Refer to Exercise 9.13. Scroll down to the portion of the applet labeled “Mean of Normal Data.” Successive observed values of a standard normal random variable can be generated and used to compute the value of the sample mean . These successive values are then plotted versus the respective sample size to obtain one “sample path.”a Do you expect the values of to cluster around any particular value? What value?b If the results of 50 sample paths are plotted, how do you expect the variability of the estimates to change as a function of sample size?c Click the button “New Sequence” several times. Did you observe what you expected based on your answers to parts (a) and (b)?ReferenceApplet Exercise Refer to Exercises 9.9–9.12. Access the applet Point Estimation.a Chose a value for p. Click the button “New Sequence” repeatedly. What do you observe?b Scroll down to the portion of the applet labeled “More Trials.” Choose a value for p and click the button “New Sequence” repeatedly. You will obtain up to 50 sequences, each based on 1000 trials. How does the variability among the estimates change as a function of the sample size? How is this manifested in the display that you obtained?ReferenceApplet Exercise Refer to Exercise 9.11. What happens if each sequence is longer? Scroll down to the portion of the screen labeled “Longer Sequences of Trials.”a Repeat the instructions in parts (a)–(c) of Exercise 9.11.b What do you expect to happen if p is not 0.5? Use the button in the lower right corner to change to value of p. Generate several sequences of trials. Comment.ReferenceApplet Exercise Refer to Exercises 9.9 and 9.10. How can the results of several sequences of Bernoulli trials be simultaneously plotted? Access the applet PointbyPoint. Scroll down until you can view all six buttons under the top graph.a Do not change the value of p from the preset value p = .5. Click the button “One Trial” a few times to verify that you are obtaining a result similar to those obtained in Exercise 9.9. Click the button “5 Trials” until you have generated a total of 50 trials. What is the value of that you obtained at the end of this first sequence of 50 trials?b Click the button “New Sequence.” The color of your initial graph changes from red to green. Click the button “5 Trials” a few times. What do you observe? Is the graph the same as the one you observed in part (a)? In what sense is it similar?c Click the button “New Sequence.” Generate a new sequence of 50 trials. Repeat until you have generated five sequences. Are the paths generated by the five sequences identical? In what sense are they similar?ReferenceApplet Exercise Refer to Exercise 9.9. Scroll down to the portion of the screen labeled “Try different probabilities.” Use the button labeled “p =” in the lower right corner of the display to change the value of p to a value other than .5.a Click the button “One Trial” a few times. What do you observe?b Click the button “100 Trials” a few times. What do you observe about the values of as the number of trials gets larger?ReferenceApplet Exercise How was Figure 9.1 obtained? Access the applet PointSingle at academic. cengage.com/statistics/wackerly. The top applet will generate a sequence of Bernoulli trials times. How many trials n have you simulated? What value of did you observe? Is the value close to .5, the true value of p? Is the graph a flat horizontal line? Why or why not?c Click the button “100 Trials” a single time. What do you observe? Click the button “100 Trials” repeatedly until the total number of trials is 1000. Is the graph that you obtained identical to the one given in Figure 9.1? In what sense is it similar to the graph in Figure 9.1?d Based on the sample of size 1000,what is the value of ? Is this value what you expected to observe?e Click the button “Reset.” Click the button “100 Trials” ten times to generate another sequence of values for .Comment.” is broken down into a number of easy to follow steps, and 685 words. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. The full step-by-step solution to problem: 14E from chapter: 9 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM.

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Applet Exercise Refer to Exercise 9.13. Scroll down to the