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 8.6 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 bar and the sample standard deviation s. (in mg/dl; round your answers to two decimal places.)

(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

upper limit

(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.

I have everything but the standard deviation s...and only a basic calculator

Answer 1

a)

Explanation: The mean and standard deviation are obtained in excel using the function =AVERAGE() and =STDEV(). The screenshot is shown below,

b)

The confidence interval for mean is obtained using the formula,

From the data values,

The t critical value is obtained from t distribution table for significance level = 0.001 and degree of freedom = n -1 = 10 - 1 = 9.

c)

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

Explanation: Since the calcium deficiency level is less than the lower limit of the 99.9% confidence interval, we can say that patient no longer has a calcium deficiency.