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, respectively, 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 \(\frac{\bar{x}-{{\mu }_{0}}}{s/\sqrt{n}}=-1.52\) and a one-sample t test is performed based on seven subjects. What is the two-tailed p-value?

7.4 Suppose the sample standard deviation of serum creatinine in Problem 7.1 is 0.6 g/dL. Assume that the standard deviation of serum creatinine is not known, and perform the hypothesis test in Problem 7.1. Report a p-value.

7.5 Compute a two-sided 95% CI for the true mean serum-creatinine level in Problem 7.4.

7.6 How does your answer to Problem 7.5 relate to your answer to Problem 7.4?

Nutrition

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary assessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9- to 11-year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population.

7.33 State the hypotheses that we can use to consider this question.

7.34 Carry out the hypothesis test in Problem 7.33 using the critical-value method with an α level of .05, and summarize your findings.

7.35 What is the p-value for the test conducted in Problem 7.34?

Ophthalmology

Researchers have reported that the incidence rate of cataracts may be elevated among people with excessive exposure to sunlight. To confirm this, a pilot study is conducted

among 200 people ages 65–69 who report an excessive tendency to burn on exposure to sunlight. Of the 200 people, 4 develop cataracts over a 1-year period. Suppose the

expected incidence rate of cataracts among 65- to 69-yearolds is 1% over a 1-year period.

7.47 What test procedure can be used to compare the 1-year rate of cataracts in this population with that in the general population?

7.48 Implement the test procedure in Problem 7.47, and report a p-value (two-sided).

7.49 Test the hypothesis that the 5-year incidence rate of cataracts is different in the excessive-sunlight-exposure group compared with the general population, and report a

p-value (two-sided).

7.50 Construct a 95% CI for the 5-year true rate of cataracts among the excessive-sunlight-exposure group.

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