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 9.6 10.7 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 and the sample standard deviation s. (in mg/dl; 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. (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

The statistical software output for this problem is:

Hence,

a) Mean = 10.17 mg/dl

s = 0.93 mg/dl

b) 99.9% confidence interval:

Lower limit = 8.76 mg/dl

Upper limit = 11.58 mg/dl

c) Since the entire confidence interval is above 6, this confidence interval suggests that the patient no longer has a calcium deficiency.

Option D is correct.