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Stats problems- chapter 5 6 7 8 9

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Question;Chapter;5;1.;Total cholesterol in children aged 10-15 is assumed to;follow a normal distribution with a mean of 191 and a standard deviation of;22.4.;What proportion of children;10-15 years of age have total cholesterol between 180 and 190?;What proportion of children;10-15 years of age would be classified as hyperlipidemic (Assume that;hyperlipidemia is defined as a total cholesterol level over 200)?;What is the 90th;percentile of cholesterol?;2.;Among coffee drinkers, men drink a mean of 3.2 cups per day;with a standard deviation of 0.8 cups.;Assume the number of coffee drinks per day follows a normal;distribution.;What proportion drink 2 cups;per day or more?;What proportion drink no more;than 4 cups per day?;If the top 5% of coffee drinkers;are considered heavy coffee drinkers, what is the minimum number of cups;consumed by a heavy coffee drinker?;Hint: Find the 95th;percentile.;3.;A study is conducted to assess the impact of caffeine;consumption, smoking, alcohol consumption and physical activity on;cardiovascular disease. Suppose that 40%;of participants consume caffeine and smoke.;If 8 participants are evaluated, what is the probability that;Exactly half of them consume;caffeine and smoke?;At most 6 consume caffeine and;smoke?;4.;A recent study of cardiovascular risk factors reported that;30% of adults met criteria for hypertension.;If 15 adults are assessed, what is the probability that;Exactly 5 meet the criteria for;hypertension?;None meet the criteria for;hypertension?;Less than or equal to 7 meet;the criteria for hypertension?;5.;Diastolic blood pressures are assumed to follow a normal;distribution with a mean of 85 and a standard deviation of 12.;What proportion of people have;diastolic blood pressure less than 90?;What proportion have diastolic;blood pressures between 80 and 90?;If someone has a diastolic;blood pressure of 100, what percentile is he/she in?;Chapter;6.;Probl. 1. (In unit 6, practice problem 1;there is a mistake in the question. Instead;of ? adults? work the problem for ?children?.;A study is run to estimate the mean total;cholesterol level in children 2-6 years of age. A sample of 9 participants is;selected and their total cholesterol levels are measured as follows;185 225 240 196 175 180 194 147;Generate a 95% confidence interval for the;true mean total cholesterol level in children. 6.6 Practice Problems;1. A;study is run to estimate the mean total cholesterol level in children 2-6 years;of age. A sample of 9 participants is;selected and their total cholesterol levels are measured as follows.;185 225 240 196 175 180 194 147 223;Generate a 95% confidence interval for the;true mean total cholesterol levels in adults with a history of hypertension.;2. A;clinical trial is planned to compare an experimental medication designed to;lower blood pressure to a placebo.;Before starting the trial, a pilot study is conducted involving 10;participants. The objective of the study;is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at;baseline and again 4 weeks later.;Compute a 95% confidence interval for the difference in blood pressures;over 4 weeks.;Baseline;120 145 130 160 152;143 126 121 115 135;4 Weeks;122 142 135 158 155 140 130 120 124 130;3. After;the pilot study (described in #2), the main trial is conducted and involves a;total of 200 patients. Patients are;enrolled and randomized to receive either the experimental medication or the;placebo. The data shown below are data;collected at the end of the study after 6 weeks on the assigned treatment.;Experimental;(n=100) Placebo (n=100);% Hypertensive 14% 22%;Generate a 95% confidence interval for the;difference in proportions of patients;with hypertension between groups.;4. The;following data were collected as part of a study of coffee consumption among;male and female undergraduate students.;The following reflect cups per day consumed;Male 3 4 6 3 2 1 0 2;Female 5 3 1 2 0 4 3 1;Generate a 95% confidence interval for the;difference in mean numbers of cups of;coffee consumed between men and women.;5. A;clinical trial is conducted comparing a new pain reliever for arthritis to a;placebo. Participants are randomly;assigned to receive the new treatment or a placebo. The outcome is pain relief within 30;minutes. The data are shown below.;Pain;Relief No Pain Relief;New Medication 44 76;Placebo 21 99;a. Generate;a 95% confidence interval for the proportion of patients on the new medication;who report pain relief;b. Generate;a 95% confidence interval for the difference in proportions of patients who;report pain relief.;Chapter;7;1. The;following data were collected in a clinical trial evaluating a new compound;designed to improve wound healing in trauma patients. The new compound was compared against a;placebo. After treatment for 5 days with;the new compound or placebo the extent of wound healing was measured and the;data are shown below.;Percent;Wound Healing;Treatment 0-25% 26-50% 51-75% 76-100%;New Compound (n=125) 15 37 32 41;Placebo (n=125) 36 45 34 10;Is there a difference in the extent of;wound healing by treatment? (Hint: Are treatment and the percent wound healing;independent?) Run the appropriate test;at a 5% level of significance.;2. Use;the data in Problem #1 and pool the data across the treatments into one sample;of size n=250. Use the pooled data to;test whether the distribution of the percent wound healing is approximately;normal. Specifically, use the following;distribution: 30%, 40%, 20% and 10% and?=0.05 to run the appropriate test.;3. The;following data were collected in an experiment designed to investigate the;impact of different positions of the mother on fetal heart rate. Fetal heart rate is measured by ultrasound in;beats per minute. The study included 20;women who were assigned to one position and had the fetal heart rate measured;in that position. Each woman was between;28-32 weeks gestation. The data are;shown below.;Back Side Sitting Standing;20 21 24 26;24 23 25 25;26 25 27 28;21 24 28 29;19 16 24 25;Is there a significant difference in mean;fetal heart rates by position? Run the;test;at a 5% level of significance.;4. A;clinical trial is conducted comparing a new pain reliever for arthritis to a;placebo. Participants are randomly;assigned to receive the new treatment or a placebo and the outcome is pain;relief within 30 minutes. The data are;shown below.;Pain;Relief No Pain Relief;New Medication 44 76;Placebo 21 99;Is there a significant difference in the;proportions of patients reporting pain relief?;Run the test at a 5% level of significance.;5. A;clinical trial is planned to compare an experimental medication designed to;lower blood pressure to a placebo.;Before starting the trial, a pilot study is conducted involving 7;participants. The objective of the study;is to assess how systolic blood pressure changes over time untreated. Systolic blood pressures are measured at;baseline and again 4 weeks later Is there a statistically significant;difference in blood pressures over time?;Run the test at a 5% level of significance.;Baseline 120 145 130 160 152;143 126;4 Weeks 122 142 135 158 155 140 130;6. A;hypertension trial is mounted and 12 participants are randomly assigned to;receive either a new treatment or a placebo.;Each participant takes the assigned medication and their systolic blood;pressure (SBP) is recorded after 6 months on the assigned treatment. The data are as follows.;Placebo New;Treatment;134 114;143 117;148 121;142 124;150 122;160 128;Is there a difference in mean SBP between;treatments? Run the appropriate test at;?=0.05.;Chapter;8;1. Suppose;we want to design a new placebo-controlled trial to evaluate an experimental;medication to increase lung capacity.;The primary outcome is peak expiratory flow rate, a continuous variable;measured in liters per minute. The;primary outcome will be measured after 6 months on treatment. The expected peak expiratory flow rate in;adults is 300 with a standard deviation of 50. How many subjects should be;enrolled to ensure 80% power to detect a difference of 15 liters per minute;with a two sided test and?=0.05?;2. An;investigator wants to estimate caffeine consumption in high school;students. How many students would be;required to ensure that a 95% confidence interval estimate for the mean;caffeine intake (measured in mg) is within 15 units of the true mean? Assume that the standard deviation in;caffeine intake is 68 mg.;3. Consider;the study proposed in problem #2. How;many students would be required to estimate the proportion of students who;consume coffee? Suppose we want the;estimate to be within 5% of the true proportion with 95% confidence.;4. A;clinical trial was conducted comparing a new compound designed to improve wound;healing in trauma patients to a placebo.;After treatment for 5 days, 58% of the patients taking the new compound;had a substantial reduction in the size of their wound as compared to 44% in;the placebo group. The trial failed to;show significance. How many subjects;would be required to detect the difference in proportions observed in the trial;with 80% power? A two sided test is;planned at?=0.05.;5. A;crossover trial is planned to evaluate the impact of an educational;intervention program to reduce alcohol consumption in patients determined to be;at risk for alcohol problems. The plan;is to measure alcohol consumption (the number of drinks on a typical drinking;day) before the intervention and then again after participants complete the;educational intervention program. How;many participants would be required to ensure that a 95% confidence interval;for the mean difference in the number of drinks is within 2 drinks of the true;mean? Assume that the standard deviation;of the difference in the mean number of drinks is 6.7 drinks.;6. An;investigator wants to design a study to estimate the difference in the;proportions of men and women who develop early onset cardiovascular disease;(defined as cardiovascular disease before age 50). A study conducted 10 years ago, found that;15% and 8% of men and women, respectively, developed early onset cardiovascular;disease. How many men and women are;needed to generate a 95% confidence interval estimate for the difference in;proportions with a margin of error not exceeding 4%?;7. The;mean body mass index (BMI) for boys age 12 is 23.6. An investigator wants to test if the BMI is;higher in boys age 12 living in New York City.;How many boys are needed to ensure that a two-sided test of hypothesis;has 80% power to detect an increase in BMI of 2 units? Assume that the standard deviation in BMI is;5.7.;8. An;investigator wants to design a study to estimate the difference in the mean BMI;between boys and girls age 12 living in New York City. How many boys and girls are needed to ensure;that a 95% confidence interval estimate for the difference in mean BMI between;boys and girls has a margin of error not exceeding 2 units? Use the estimate of the variability in BMI;from problem #7.;Chapter;9;1. Consider;the following data measured in a sample of n=25 undergraduates in an on-campus;survey of health behaviors. Enter the data into an Excel worksheet for;analysis.;ID;Age;Female Sex;Year in School;GPA;Current Smoker;# Hours Exercise per Week;# Average Number of Drinks per Week;# Cups Coffee per Week;1;18;1;Fr;3.85;1;7;3;3;2;21;0;Jr;3.27;1;3;2;4;3;19;1;So;2.90;0;0;4;7;4;22;0;Sr;3.65;1;0;2;4;5;21;1;Sr;3.41;1;0;1;3;6;20;0;Jr;3.20;0;2;5;8;7;19;1;Jr;2.89;1;1;4;10;8;17;0;Fr;3.75;0;6;0;0;9;18;0;So;4.00;0;6;2;6;10;17;1;So;3.18;0;3;5;7;11;21;0;Jr;2.58;1;3;12;12;12;22;1;Sr;2.98;0;2;3;4;13;19;0;Fr;3.16;1;2;0;6;14;21;1;Jr;3.36;1;3;1;2;15;22;1;So;3.72;0;6;3;0;16;19;0;So;3.30;1;4;0;6;17;16;0;Fr;3.28;0;4;0;5;18;22;0;Sr;2.98;0;0;8;5;19;17;1;Fr;3.90;0;7;0;2;20;20;1;Sr;3.78;1;4;6;2;21;21;1;So;3.26;1;2;3;4;22;23;0;Jr;3.01;0;1;9;7;23;23;0;Sr;3.83;1;5;4;4;24;17;1;Fr;3.76;0;5;2;1;25;22;1;Sr;3.05;0;1;5;5;2. Estimate;the simple linear regression equation relating number of cups of coffee per;week to GPA (Consider GPA the dependent or outcome variable).;3. Estimate;the simple linear regression equation relating female sex to GPA (Consider GPA;the dependent or outcome variable).;4. Estimate;the multiple linear regression equation relating number of cups of coffee per;week, female sex and number of hours of exercise per week to GPA (Consider GPA;the dependent or outcome variable).

 

Paper#62358 | Written in 18-Jul-2015

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