Question

# A laboratory claims that the mean sodium level, ? , of a healthy adult is 141...

A laboratory claims that the mean sodium level, ? , of a healthy adult is 141 mEq per liter of blood. To test this claim, a random sample of 90 adult patients is evaluated. The mean sodium level for the sample is 140 mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is 14 mEq. Can we conclude, at the 0.05 level of significance, that the population mean adult sodium level differs from that claimed by the laboratory? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: ?

The alternative hypothesis:?

The type of test statistic:?

The value of the test statistic: (Round to at least three decimal places.) ?

The p-value: (Round to at least three decimal places.)?

Can we conclude that the population mean adult sodium level differs from that claimed by the laboratory?

Solution:

Null Hypothesis (Ho): = 141

Alternative Hypothesis (Ha): 141

Since population standard deviation is known, we use Z-test.

Test Statistics

Z = (141 - 140)/ (14/90)

Z = 0.678

Using Z-tables, the p-value is

P [Z 0.678] = P [Z < -0.678] + P [Z > 0.678]

= 0.249 + 0.249

= 0.498

Since p-value is is greater than 0.05 level of significance, we fail to reject Ho.

Hence, we cannot conclude that the population mean adult sodium level differs from that claimed by the laboratory.