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 8.4 10.7 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.

Answer 1

a. Sample mean is

Create the following table.

data	data-mean	(data - mean)2
10.1	0.010	0.0000
8.4	-1.69	2.8561
10.7	0.61	0.3721
9.3	-0.79	0.6241
9.4	-0.69	0.4761
9.8	-0.29	0.0841
10.0	-0.09	0.0081
9.9	-0.19	0.0361
11.2	1.11	1.2321
12.1	2.01	4.0401

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

So standard deviation is

b. t value for 99.9% CI is TINV(0.001,9)=4.781

So Margin of ERror is

Hence CI is

Lower bound is 8.52

Upper bound is 11.66

c. As 6 is not in the CI level answer here is

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