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

9.4

10.7

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

(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 is

Create the following table.

data	data-mean	(data - mean)2
10.1	-0.11	0.0121
9.4	-0.81	0.6561
10.7	0.49	0.2401
9.5	-0.71	0.5041
9.4	-0.81	0.6561
9.8	-0.41	0.1681
10.0	-0.21	0.0441
9.9	-0.31	0.0961
11.2	0.99	0.9801
12.1	1.89	3.5721

Find the sum of numbers in the last column to get.

So standard deviation is

b. t value is TINV(0.001,9)=4.781

So Margin of Error is

So CI is

c. As Upper and lower CI is greater than 6.

So answer here is Yes. This confidence interval suggests that the patient no longer has a calcium deficiency.