Question

Choo Choo Paper Company makes various types of paper products. One of their products is a 30 mils thick paper. In order to ensure that the thickness of the paper meets the 30 mils specification, random cuts of paper are selected and the thickness of each cut is measured. A sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils.

a.	Compute the standard error of the mean.
b.	At 95% confidence using the critical value approach, test to see if the mean thickness is significantly more than 30 mils.
c.	Show that the p-value approach results in the same conclusion as that of part b.

Answer 1

a)

Standard error of mean = S / sqrt(n)

= 4 / sqrt(256 )

= 0.25

b)

H0: = 30

Ha: > 30

Test statistics

t = - / S / sqrt(n)

= 30.3 - 30 / 0.25

= 1.2

t critical value at 0.05 level with 255 df = 1.651

Since test statistics t < 1.651, do not reject H0.

We conclude that we fail to support the claim that the mean thickness is significantly more than 30 mils.

c)

From T table,

With test statistics t = 1.2 and df = 255

p-value = 0.1156

Since p-value > 0.05 level , Do not reject H0.

We conclude that we fail to support the claim that the mean thickness is significantly more than 30 mils.