An article presents a study of the effect of the subbase thickness on the amount

Question

An article presents a study of the effect of the subbase thickness on the amount of surface deflection caused by aircraft landing on an airport runway. In six applications of a 170 kN load on a runway with a subbase thickness of 409 mm. the average surface deflection was 3.24 mm with a standard deviation of 0.48 mm. Can you conclude that the mean surface deflection is greater than 3 mm? Since the P-value is 0.137 6, we conclude that the mean surface deflection is greater than 3 mm. Can you conclude that the mean surface deflection is greater than 2.5 mm? Round the test statistic to four decimal places. Since the P-value is, we conclude that the mean surface deflection is greater than 2.5 mm.

Explanation / Answer

1) MEAN = 3.24

STANDARD DEVIATION = 0.48

N = 6

TEST STATIC = (X-MEAN)/(STANDARD DEV/SQRT(N))

X = 3

THEREFORE TEST STATIC = (3-3.24)/(0.48/SQRT(6)) = -1.230

THE DEGREE OF FREEDOM = 6-1 = 5

THE P VALUE WILL BE TAKEN FROM THE T TABLE

= 0.1367

IT IS NOT SIGNIFICANT FOR ALPHA = 0.05 THEREFORE WE CANNOT CONCLUDE THE MEAN DEFLECTIONIS GRETER THEN 3

B) HERE APPLYING THE SAME CONCEPT JUST THE VALU OF X WILL BE NOW = 2.5

TEST STATIC = (2.5 - 3.24)/(0.48/SQRT(6))

= -3.77

AGAIN DEGREE OF FREEDOM = 6-1 = 5

NOW THE P VALUE WILL BE TAKEN FROM T TABLE = 0.0065

WHICH IS SIGNIFICANT FOR ALPHA = 0.05

THEREFORE WE CAN CANCLUDE THAT THE MEAN DEFLECTION IS GRETAER THEN THE 2.5

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