The level of various substances in the blood of kidneydialysis patients is of co

Question

The level of various substances in the blood of kidneydialysis patients is of concern. A researcher did blood tests on adialysis patient on six consective visits. One variable measuredwas the level of phosphate in the blood. The data on this onepatient, in milligrams of phosphate per deciliter (mg/dl) of blood,are: 5.6, 5.1, 4.6, 4.8, 5.7, and 6.4 The normal range of values for blood phosphate level is 2.6 to4.8 mg/dl. a.) Report a 95% one-sided confidence interval for the meanblood phosphate level b.) What sample size would you recommend, if it important todetect and treat the elevated avearge phosphate level of 5.5? The level of various substances in the blood of kidneydialysis patients is of concern. A researcher did blood tests on adialysis patient on six consective visits. One variable measuredwas the level of phosphate in the blood. The data on this onepatient, in milligrams of phosphate per deciliter (mg/dl) of blood,are: 5.6, 5.1, 4.6, 4.8, 5.7, and 6.4 The normal range of values for blood phosphate level is 2.6 to4.8 mg/dl. a.) Report a 95% one-sided confidence interval for the meanblood phosphate level b.) What sample size would you recommend, if it important todetect and treat the elevated avearge phosphate level of 5.5?

Explanation / Answer

a.) at 95% confidence, z from the z table = 1.65
a 95% one-sided confidence interval for the mean bloodphosphate level = + ze = 3.7 + (1.65*0.27) = 4.15

b.) What sample size would you recommend, if it important todetect and treat the elevated average phosphate level of 5.5?
z = (X-)/e
hence, 1.65 = (5.5-3.7)/e
hence, e = 1.09
hence, s/n = 1.09
hence, 0.67 / n = 1.09
hence, n = 0.38

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