Question

Calcium normally occurs in the blood of mammals at concentrations of about 6 mg per 100 ml of total blood. The standard deviation of this variable is 1 mg of calcium per 100 ml of the total blood volume. A greater variability to this can cause serious disorders in the coagulation of the blood. A series of nine tests on one patient revealed a sample mean of 6.2 mg of calcium per 100 ml of total blood volume, and a standard sample deviation of 2 mg of calcium per 100 ml of blood. Is there any evidence, for a level alfa at 0.05, that the average level of calcium for this patient is higher than normal?

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 6.0
Alternative hypothesis: u > 6.0

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.667
DF = n - 1

D.F = 8
t = (x - u) / SE

t = 0.30

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 0.30.

Thus the P-value in this analysis is 0.386.

Interpret results. Since the P-value (0.386) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the average level of calcium for this patient is higher than normal.