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

8.8

10.5

8.9

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

Answer)

Using calculator

A)

Mean = 10.07

S.d = 1.0067

B)

As the population s.d is unknown we will use t table to construct the interval

Degrees of freedom is = sample size - 1, 9

For df 9 and 99.9 confidence level, critical value t is = 4.781

Margin of error (MOE) = t*(s.d/√n) = 4.781*(1.0067/√10)

MOE = 1.52201457848

Lower limit is = mean - moe = 8.54798542151 = 8.55

Upper limit is = mean + moe = 11.5920145784 = 11.59

C)

As 6 is less than the lower limit (8.55)

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