In: Statistics and Probability
An important quality characteristic used by the manufacturers of
ABC asphalt shingles is the amount of moisture the shingles contain
when they are packaged. Customers may feel that they have purchased
a product lacking in quality if they find moisture and wet shingles
inside the packaging. In some cases, excessive moisture
can cause the granules attached to the shingles for texture and
colouring purposes to fall off the shingles resulting in appearance
problems. To monitor the amount of moisture present, the company
conducts moisture tests. A shingle is weighed and then dried. The
shingle is then reweighed, and based on the amount of moisture
taken out of the product, the pounds of moisture per 100 square
feet is calculated. The company claims that the mean moisture
content cannot be greater than 0.35 pound per 100 square
feet.
The file (A & B shingles.csv) includes 36 measurements (in
pounds per 100 square feet) for A shingles and 31 for B
shingles.
3.1. For the A shingles, form the null and alternative hypothesis
to test whether the population mean moisture content is less than
0.35 pound per 100 square feet.
3.2. For the B shingles, form the null and alternative hypothesis
to test whether the population mean moisture content is less than
0.35 pound per 100 square feet.
3.3. Do you think that the population means for shingles A and B
are equal?
Form the hypothesis and conduct the test of the hypothesis.
What assumption do you need to check before the test for equality
of means is performed?
3.4. What assumption about the population distribution is needed in
order to conduct the hypothesis tests above?
A |
B |
0.44 |
0.14 |
0.61 |
0.15 |
0.47 |
0.31 |
0.3 |
0.16 |
0.15 |
0.37 |
0.24 |
0.18 |
0.16 |
0.42 |
0.2 |
0.58 |
0.2 |
0.25 |
0.2 |
0.41 |
0.26 |
0.17 |
0.14 |
0.13 |
0.33 |
0.23 |
0.13 |
0.11 |
0.72 |
0.1 |
0.51 |
0.19 |
0.28 |
0.22 |
0.39 |
0.44 |
0.39 |
0.11 |
0.25 |
0.11 |
0.16 |
0.31 |
0.2 |
0.43 |
0.22 |
0.26 |
0.42 |
0.18 |
0.24 |
0.44 |
0.21 |
0.43 |
0.49 |
0.16 |
0.34 |
0.52 |
0.36 |
0.36 |
0.29 |
0.22 |
0.27 |
0.39 |
0.4 |
|
0.29 |
|
0.43 |
|
0.34 |
|
0.37 |