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.

9.5

9.6

10.1

8.7

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 and the sample standard deviation s. (in mg/dl; round your answers to two decimal places.)
= mg/dl
s = mg/dl

(b)

Find a 99.9% confidence interval for the population mean of total calcium in this patient's blood. (in mg/dl; 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

calculate the sample mean and sample standard deviation we get,

as follows

a)

Sample size (n): 10
Mean ( ): 10.3
Standard deviation (s): 0.9638

b)

Confidence level: c = 99.9%

formula for confidence interval is

Where tc is the t critical value for c=99.9% with df=n-1 = 10-1 = 9

using t table we get critical value as

tc = 4.781

8.843<    < 11.757

lower limit = 8.843 mg/dl

upper limit = 11.757 mg/dl

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