Question

The thickness of eight pads designed for use in aircraft engine mounts are measured. The results, in mm, are 41.8, 40.9, 42.1, 41.2, 40.5, 41.1, 42.6, and 40.6. Assumed that the thicknesses are from a normal distribution. Can you conclude that the mean thickness is greater than 41.0 mm a) State your hypotheses. b) Test your hypotheses at .01 significance level. c) Your conclusion (in the context of this problem)

Answer 1

We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm

Explanation:

Sample Information:

Results:

41.8

40.9

42.1

41.2

40.5

41.1

42.6

40.6

From the table we get:

sample mean : x = 41.35

sample standard deviation s = 0.698

Hypothesis Test:

Null Hypothesis H₀ x = 41

Alternative Hypothesis Hₐ x > 41

The test is a one-tail test

If significance level is 0.01 and n = 8 we need to use t-student distribution

From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1

df = 7 t(c) = 2.998

To calculate t(s) = ( x - 41 ) / s/√n

t(s) = ( 41.35 - 41 ) / 0.698/√8

t(s) = 0.35 * 2.83/ 0.698

t(s) = 1.419

Comparing t(s) and t(c)

t(s) < t(c)

t(s) is in the acceptance region we accept H₀