Question

Over the past several months, an adult patient was treated for tetany (severe muscle spasms). This condition is associated with an average total calcium level below 6 mg/dl. Assume that blood levels of calcium are approximately normally distributed. After the treatment was complete, 9 blood tests for total calcium levels were taken on this patient which gave the following results (in mg/dl ):  7.7 9.1 7.6 8.2 8.5 9.0 9.9 10.5 9.1

For these 9 tests, x = 8.84 and s = 0.96.
a) Why should we use the t distribution for this problem as opposed to using the S. N. D. for calculating a confidence interval?

b) Find a 95% confidence interval for the population mean µ of total calcium in this patient’s blood.

c) Does it seem that this patient still has a calcium deficiency? Explain.

Answer 1