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.

9.3 8.6 10.1 8.5 9.4 9.8 10.0 9.9 11.2 12.1

(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

Answer 1

given data is :

9.3 8.6 10.1 8.5 9.4 9.8 10.0 9.9 11.2 12.1

calculate the sample mean and sample standard deviation we get,

as follows

Sample size (n): 10
Mean ( ): 9.89
Standard deviation (s): 1.0979

Confidence level: c = 99.9%

formula for confidence interval is

Where tc is the t critical value for c=99.9% with df=n-1 = 10-1 = 9

using t table we get critical value as

tc = 4.781

8.2301 <    < 11.5499

lower limit = 8.23 mg/dl

upper limit = 11.55 mg/dl