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. 9.9 9.0 10.3 9.1 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

From the given sample data : n=10 , ,

(a)

mg/dl

Standard deviation = mg/dl

(b) The 99.9% confidence interval for population mean of total calcium in this patient's blood is ,

; , From excel "=TINV(0.001,9"

Lower limit=8.63 mg/dl

Upper limit=11.51 mg/dl

Since , Hypothesis : Vs  

Decision : Here , the hypothesized value does not lies in the confidence interval.

Therefore , reject the null hypothesis.

Conclusion: Yes. This confidence interval suggests that the patient may still have a calcium deficiency.