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. 10.1 8.6 10.3 9.1 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 (c) Based on your results in part (b), do you think this patient still has a calcium deficiency? Explain. Yes. This confidence interval suggests that the patient may still have a calcium deficiency. Yes. This confidence interval suggests that the patient no longer has a calcium deficiency. No. This confidence interval suggests that the patient may still have a calcium deficiency. No. This confidence interval suggests that the patient no longer has a calcium deficiency.

Answer 1

a)

sample mean, xbar = 10.05
sample standard deviation, s = 1.01

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) = 4.78

ME = tc * s/sqrt(n)
ME = 4.78 * 1.01/sqrt(10)
ME = 1.527

CI = (10.05 - 4.78 * 1.01/sqrt(10) , 10.05 + 4.78 * 1.01/sqrt(10))
CI = (8.52 , 11.58)

Lower limit = 8.52
Upper limit = 11.58

c)
No. This confidence interval suggests that the patient no longer has a calcium deficiency.