Question

A laboratory claims that the mean sodium level,

μ

, of a healthy adult is

139

mEq per liter of blood. To test this claim, a random sample of

150

adult patients is evaluated. The mean sodium level for the sample is

138

mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is

13

mEq. Can we conclude, at the

0.1

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: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.) The two critical values at the 0.1 level of significance: (Round to at least three decimal places.) and Can we conclude that the population mean adult sodium level differs from that claimed by the laboratory? Yes No

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 139

H_a : 139

Test statistic = z

= ( - ) /    / n

= (138 -137) / 13 / 150

= -0.942

Test statistic = -0.942

P-value = 0.3461

= 0.1

Critical value = -1.645 , +1.645

No