Perform a twotailed test Then fill in the table below Carry

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)

Z

t

Chi square

F

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

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

Yes

No

A laboratory claims that the mean sodium level, , of a healthy adult is mEq per liter of blood. To test this claim, a random sample of adult patients is evaluated. The mean sodium level for the sample is mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is mEq. Can we conclude, at the 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.)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   139   [ANSWER]
Ha:    u   =/   139   [ANSWER]

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We use Z DISTRIBUTION, as n is large, n = 150.

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Getting the test statistic, as              
              
X = sample mean =    136          
uo = hypothesized mean =    139          
n = sample size =    150          
s = standard deviation =    15          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.449489743 [ANSWER, TEST STATISIC]

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As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha/2 =    0.005          
zcrit =    +/-   2.575829304   [ANSWER, CRITICAL VALUES]

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Also, the p value is              
              
p =    0.014305878          
              
Comparing z and zcrit (or, p and significance level), we   FAIL TO REJECT THE NULL HYPOTHESIS.          
Hence, NO: We cannot conclude that the population mean adult sodium level differs from that claimed by the laboratory. [ANSWER, NO]

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