Question

Give an example in the real world where you might do a t-test. Explain what your sample and population averages might be.

Answer 1

let us discussed 1 - sample t test example .

Average size of barnacle shell is 25 mm . we take 10 barnacles were collected in south India and their sizes are (mm) 22,23,22,25,28,27,28,25,23,21 .

Are these south India barnacles are of small sizes ? with = 5 %

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where population mean() is 25 mm

and sample mean = = (22+23+22+25+28+27+28+25+23+21)/10=24.4

s =

s =2.590581

we want to test hypothesis

Ho : =25

Ha : < 25

test statistics =    ~ t _n-1

Test statistic = -0.7377

t table = t _{n-1 ,0.05} =1.833

Decision Rule ; we accept H0 if test statistic < table value Average size of barnacle shell is 25 mm

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Thank You !

Conclusion : here -0.7377 < 1.833 so we accept Ho , i.e.