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.

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:

H0<=0.35

HA>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 feet is given:

H0<=0.35

HA>0.35

3.1 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?

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

Shingles -A 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 Shingles -B 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

kindly let us know the steps and solution including P Value, if this is a unpaired or Paired test, and if this is a one tail or 2 tail test, also let us know if we need to perform Mannwhitneyu?