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7.7 Use a computer program to compute the probability that a t distribution with 36 df exceeds 2.5.

7.7 Use a computer program to compute the probability that a t distribution with 36 df exceeds 2.5.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please answer 7.7-7.9 using R

PROBLEMS Renal Disease The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. *7.1 If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respec- tively, then, using a significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population. *7.2 What is the p-value for the test? *7.3 Suppose the sample standard deviation of serum cre- atinine in Problem 7.1 is 0.6 mg/dL. Assume that the stan- dard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value. *7.4 Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.3. *7.5 How does your answer to Problem 7.4 relate to your answer to Problem 7.3. 7.6 Suppose x-Ho s/√n = -1.52 and a one-sample t test is performed based on seven subjects. What is the two-tailed p-value? 7.7 Use a computer program to compute the probability that a t distribution with 36 df exceeds 2.5. 7.8 Use a computer program to compute the lower 10th percentile of a t distribution with 54 df. Diabetes Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean In (plasma-glucose) concen- tration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lowe level of plasma glucose than the general population. 7.9 If the expected difference is 0.10 In units, then what is the power of such a study if a two-sided test is to be used with α = .05? 7.10 Answer Problem 7.9 if the expected difference is 0.20 In units. 7.11 How many people would need to be studied to have 80% power under the assumptions in Problem 7.9? Cardiovascular Disease Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Problems 269 7.12 Using the critical-value method with a = .05, test the hypothesis that incidence rates of MI changed from 2000 to 2010. 7.13 Report a p-value to correspond to your answer to Problem 7.12. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate. 7.14 Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour case- fatality rate changed from 2000 to 2010. 7.15 Suppose we eventually plan to accumulate 50 MI cases during the period 2010-2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010-2015 if a two-sided test with significance level .05 is planned? 7.16 How large a sample is needed in Problem 7.15 to achieve 90% power? Pulmonary Disease Suppose the annual incidence of asthma in the general population among children 0-4 years of age is 1.4% for boys and 1% for girls. *7.17 If 10 cases are observed over 1 year among 500 boys 0-4 years of age with smoking mothers, then test whether there is a significant difference in asthma incidence between this group and the general population using the critical-value method with a two-sided test. *7.18 Report a p-value corresponding to your answer to Problem 7.17. *7.19 Suppose that four cases are observed over 1 year among 300 girls 0-4 years of age with smoking mothers. Answer Problem 7.17 based on these data. *7.20 Report a p-value corresponding to your answer to Problem 7.19. Genetics Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A's in the 20th position. 7.21 If the probability of an A in the 20th position in ribosomal 5S RNA is .79, then test the hypothesis that the new sequence is the same as ribosomal 5S RNA using the critical-value method.
Transcribed Image Text:PROBLEMS Renal Disease The mean serum-creatinine level measured in 12 patients 24 hours after they received a newly proposed antibiotic was 1.2 mg/dL. *7.1 If the mean and standard deviation of serum creatinine in the general population are 1.0 and 0.4 mg/dL, respec- tively, then, using a significance level of .05, test whether the mean serum-creatinine level in this group is different from that of the general population. *7.2 What is the p-value for the test? *7.3 Suppose the sample standard deviation of serum cre- atinine in Problem 7.1 is 0.6 mg/dL. Assume that the stan- dard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value. *7.4 Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.3. *7.5 How does your answer to Problem 7.4 relate to your answer to Problem 7.3. 7.6 Suppose x-Ho s/√n = -1.52 and a one-sample t test is performed based on seven subjects. What is the two-tailed p-value? 7.7 Use a computer program to compute the probability that a t distribution with 36 df exceeds 2.5. 7.8 Use a computer program to compute the lower 10th percentile of a t distribution with 54 df. Diabetes Plasma-glucose levels are used to determine the presence of diabetes. Suppose the mean In (plasma-glucose) concen- tration (mg/dL) in 35- to 44-year-olds is 4.86 with standard deviation = 0.54. A study of 100 sedentary people in this age group is planned to test whether they have a higher or lowe level of plasma glucose than the general population. 7.9 If the expected difference is 0.10 In units, then what is the power of such a study if a two-sided test is to be used with α = .05? 7.10 Answer Problem 7.9 if the expected difference is 0.20 In units. 7.11 How many people would need to be studied to have 80% power under the assumptions in Problem 7.9? Cardiovascular Disease Suppose the incidence rate of myocardial infarction (MI) was 5 per 1000 among 45- to 54-year-old men in 2000. To look at changes in incidence over time, 5000 men in this age group were followed for 1 year starting in 2010. Fifteen new cases of MI were found. Problems 269 7.12 Using the critical-value method with a = .05, test the hypothesis that incidence rates of MI changed from 2000 to 2010. 7.13 Report a p-value to correspond to your answer to Problem 7.12. Suppose that 25% of patients with MI in 2000 died within 24 hours. This proportion is called the 24-hour case-fatality rate. 7.14 Of the 15 new MI cases in the preceding study, 5 died within 24 hours. Test whether the 24-hour case- fatality rate changed from 2000 to 2010. 7.15 Suppose we eventually plan to accumulate 50 MI cases during the period 2010-2015. Assume that the 24-hour case-fatality rate is truly 20% during this period. How much power would such a study have in distinguishing between case-fatality rates in 2000 and 2010-2015 if a two-sided test with significance level .05 is planned? 7.16 How large a sample is needed in Problem 7.15 to achieve 90% power? Pulmonary Disease Suppose the annual incidence of asthma in the general population among children 0-4 years of age is 1.4% for boys and 1% for girls. *7.17 If 10 cases are observed over 1 year among 500 boys 0-4 years of age with smoking mothers, then test whether there is a significant difference in asthma incidence between this group and the general population using the critical-value method with a two-sided test. *7.18 Report a p-value corresponding to your answer to Problem 7.17. *7.19 Suppose that four cases are observed over 1 year among 300 girls 0-4 years of age with smoking mothers. Answer Problem 7.17 based on these data. *7.20 Report a p-value corresponding to your answer to Problem 7.19. Genetics Ribosomal 5S RNA can be represented as a sequence of 120 nucleotides. Each nucleotide can be represented by one of four characters: A (adenine), G (guanine), C (cytosine), or U (uracil). The characters occur with different probabilities for each position. We wish to test whether a new sequence is the same as ribosomal 5S RNA. For this purpose, we replicate the new sequence 100 times and find there are 60 A's in the 20th position. 7.21 If the probability of an A in the 20th position in ribosomal 5S RNA is .79, then test the hypothesis that the new sequence is the same as ribosomal 5S RNA using the critical-value method.
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