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 are calculated. The company would like to show that the mean moisture content is less than 0.35 pound per 100 square feet.
Answers
Answer:
Explanation:
3.1Problem Do you think there is evidence that mean moisture contents in both types of shingles are within the permissible limits? State your conclusions clearly showing all steps.
Solution:
Input - Python Jupyter
t_statistic, p_value = ttest_1samp(df.A, 0.35)
print('One sample t test \nt statistic: {0} p value: {1} '.format(t_statistic, p_value/2))
Output from Python Jupyter
One sample t test
t statistic: -1.4735046253382782 p value: 0.07477633144907513
Since pvalue > 0.05, do not reject H0 . There is not enough evidence to conclude that the mean moisture content for Sample A shingles is less than 0.35 pounds per 100 square feet. p-value = 0.0748. If the population mean moisture content is in fact no less than 0.35 pounds per 100 square feet, the probability of observing a sample of 36 shingles that will result in a sample mean moisture content of 0.3167 pounds per 100 square feet or less is .0748.
Input - Python Jupyter
t_statistic, p_value = ttest_1samp(df.B, 0.35,nan_policy='omit' )
print('One sample t test \nt statistic: {0} p value: {1} '.format(t_statistic, p_value/2))
Output from Python Jupyter
One sample t test
t statistic: -3.1003313069986995 p value: 0.0020904774003191826
Since pvalue < 0.05, reject H0 . There is enough evidence to conclude that the mean moisture content for Sample B shingles is not less than 0.35 pounds per 100 square feet. p-value = 0.0021. If the population mean moisture content is in fact no less than 0.35pounds per 100 square feet, the probability of observing a sample of 31 shingles that will result in a sample mean moisture content of 0.2735 pounds per 100 square feet or less is .0021.
3.2 Problem 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?
Solution:
H0 : μ(A)= μ(B)
Ha : μ(A)!= μ(B)
α = 0.05
Input - Python Jupyter
t_statistic,p_value=ttest_ind(df['A'],df['B'],equal_var=True ,nan_policy='omit')
print("t_statistic={} and pvalue={}".format(round(t_statistic,3),round(p_value,3)))
Output from Python Jupyter
t_statistic=1.29 and pvalue=0.202
As the pvalue > α , do not reject H0; and we can say that population mean for shingles A and B are equal Test Assumptions When running a two-sample t-test, the basic assumptions are that the distributions of the two populations are normal, and that the variances of the two distributions are the same. If those assumptions are not likely to be met, another testing procedure could be use.
Explanation: