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 companyclaimsthat the mean moisture contentcannot be greaterthan 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.

For the A shingles, the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feetis given:

<=0.35

>0.35

For the B shingles, the null and alternative hypothesis to test whether the population mean moisture content is less than 0.35 pound per 100 square feetis given:

<=0.35

>0.35

3.1 Do you think that the population means for shingles A and B are equal? Formthe hypothesis and conductthe test of the hypothesis. What assumption do you need to check before the test for equality of means is performed?

3.2 What assumption about the population distribution is needed in order to conduct the hypothesis tests above?

A Data

0.44 0.61 0.47 0.3 0.15 0.24 0.16 0.2 0.2 0.2 0.26 0.14 0.33 0.13 0.72 0.51 0.28 0.39 0.39 0.25 0.16 0.2 0.22 0.42 0.24 0.21 0.49 0.34 0.36 0.29 0.27 0.4 0.29 0.43 0.34 0.37

B Data

0.14 0.15 0.31 0.16 0.37 0.18 0.42 0.58 0.25 0.41 0.17 0.13 0.23 0.11 0.1 0.19 0.22 0.44 0.11 0.11 0.31 0.43 0.26 0.18 0.44 0.43 0.16 0.52 0.36 0.22 0.39