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.

9.7 9.2 10.5 8.7 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

Answer 1

a)

We need to calculate mean and SD, preparing table for that

	X	X2
	9.7	94.09
	9.2	84.64
	10.5	110.25
	8.7	75.69
	9.4	88.36
	9.8	96.04
	10	100
	9.9	98.01
	11.2	125.44
	12.1	146.41
Sum =	100.5	1018.93

Mean is calculated as

Variance is calculated as

Sd is given by

Mean = 10.05

s = 0.995

b)

To calculate 99.9% confidence interval, we need to find tc (Critical t value) as population standard deviation is not given

For 99.9% CI and dof = n-1 = 10-1 = 9, tc = 4.781

Confidence Interval is given by

Lower limit: 8.546

Upper Limit: 11.554