Lung capacity is important for a SCUBA diver. This is measured as FVC (forced vi

Question

Lung capacity is important for a SCUBA diver.  This is measured as FVC (forced vital capacity measured in litres) which is the volume of air that a person can force out of their lungs.  A researcher developed the following research question: Is the FVC of smokers less than the FVC of a healthy population (a healthy population is known to have a mean FVC of 5.2 L).  To test this hypothesis, 26 smokers were randomly chosen and their FVC measured.  This data is recorded in the Minitab worksheet indicated above in the column titled: FVC_smokers (L).  Test the researcher’s hypothesis at the 10% level of significance.

FVC_Smokers
4.9
3.5
4.2
4.9
4.6
4.8
4.4
4.6
4.3
3.8
4.8
4.3
3.8
4.3
4.2
3.9
4.5
4.6
4.7
3.6
4.3
4.7
4.0
4.3
4.8
4.0

1.

Which test statistic must you use (Z or t)?

Type the correct test statistic (enter Z or t )

2.

What is the value of the test statistic?  (Round to 2 decimal places if using Z, but round to 3 decimal places if using t)

Explanation / Answer

Mean of the data=4.338462

stddev=0.403065

We use t statistic as the sample size <30

test stat=(4.338462-5.2)/(0.403065/sqrt(26))=-14.793

As t is very large,we reject H0 and accept our claim that the FVC of the healthy population is Less than 5.2

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