Question

# Over the past several months, an adult patient has been treated for tetany (severe muscle spasms)....

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.

 9.3 9 10.7 9.3 9.4 9.8 10 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.

 Values ( X ) Σ ( Xi- X̅ )2 9.3 0.5929 9 1.1449 10.7 0.3969 9.3 0.5929 9.4 0.4489 9.8 0.0729 10 0.0049 9.9 0.0289 11.2 1.2769 12.1 4.1209 Total 100.7 8.681

Part a)

Mean X̅ = Σ Xi / n
X̅ = 100.7 / 10 = 10.07

Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 8.681 / 10 -1 ) = 0.98

Part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.001 /2, 10- 1 ) = 4.781
10.07 ± t(0.001/2, 10 -1) * 0.98/√(10)
Lower Limit = 10.07 - t(0.001/2, 10 -1) 0.98/√(10)
Lower Limit = 8.5884 ≈ 8.59
Upper Limit = 10.07 + t(0.001/2, 10 -1) 0.98/√(10)
Upper Limit = 11.5516 ≈ 11.55
99.9% Confidence interval is ( 8.59 , 11.55 )

Part c)

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

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