Over the past several months, an adult patient has been treated for tetany (seve

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. 9.5 8.6 10.3 8.5 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.) 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 upper limit mg/dl mg/dl

Explanation / Answer

sample mean = ( ? xi ) / n, Here n=9 and  ? xi=99.3

sample mean=9.93

sample standard deviation ?=square root ((1/(n?1))*?(xi??x?)^2)
substituting the values we get,
standard deviation=1.09

z value for 99.9% confidence interval is 3.291

99.9% confidence interval for sample mean is:

upper limit=sample mean+(3.291*(standard deviation)/?n))=11.06

lower limit=sample mean-(3.291*(standard deviation)/?n))=8.79

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