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

9.0

10.9

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 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) Using TI 84 calculator

enter the data set in L1 list

then click on calc and select 1 var stat

we get

mean = 10.05

standard deviation = 1.05

(B) using TI 84 calculator

press stat then tests then select TInterval

enter the data

xbar = 10.05

s = 1.05

n = 10

c-level = 0.99

press calculate

we get

99% confidence interval = (8.97, 11.13)

(C) We can see that the 99% confidence interval is (8.97, 11.13). Lower limit of confidence interval is above 6, so there is no deficiency

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