Question

Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Recently, the patient's total calcium tests gave the following readings (in mg/dl). Assume that the population of x values has an approximately normal distribution.

9.7

9.0

10.1

9.5

9.4

9.8

10.0

9.9

11.2

12.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean reading x and the sample standard deviation s. (Round your answers to two decimal places.)

x =	____mg/dl
s =	____mg/dl

(b) Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (Round your answer to two decimal places.)

lower limit	mg/dl
upper limit	mg/dl

Answer 1

a)

sample mean, xbar = 10.07
sample standard deviation, s = 0.92

b)

sample size, n = 10
degrees of freedom, df = n - 1 = 9

Given CI level is 99.9%, hence α = 1 - 0.999 = 0.001
α/2 = 0.001/2 = 0.0005, tc = t(α/2, df) = 4.781

ME = tc * s/sqrt(n)
ME = 4.781 * 0.92/sqrt(10)
ME = 1.391

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (10.07 - 4.781 * 0.92/sqrt(10) , 10.07 + 4.781 * 0.92/sqrt(10))
CI = (8.68 , 11.46)

lower limit = 8.68     mg/dl
upper limit = 11.46    mg/dl