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.
9.5 | 8.4 | 10.3 | 9.3 | 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.
a)
x = 9.99
s = 1.04
b)
sample mean, xbar = 9.99
sample standard deviation, s = 1.04
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
CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (9.99 - 4.781 * 1.04/sqrt(10) , 9.99 + 4.781 *
1.04/sqrt(10))
CI = (8.42 , 11.56)
c)
No. This confidence interval suggests that the patient no longer
has a calcium deficiency.
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