A certain company receives shipments of the same liquid (substance XY-135) from Company A and Company B, respectively. Company A and Company B both ship this substance XY-135 in barrels with carrying capacity of eleven gallons. The company wants to test whether there is a difference in the amount of substance XY-135 received by barrels from Company A and Company B, respectively. A sample size of n = 15 barrels is collected from Company A, with a mean of 10.711 gallons and standard deviation of 3.4 gallons, while a sample of size n = 19 barrels is collected from Company B with a mean of 9.910 gallons with standard deviation of 3.2 gallons, respectively. Additionally, a sample mean difference of 2.100 was calculated with a sample standard deviation of the difference, sd, calculated to be 5.831. Furthermore, a Shapiro Wilk Test for Normality was conducted on the sample from Company A and the sample from Company B, and p-values of p = .1492 and p = 9632 were obtained, respectively. Using a = 0.05, conduct a hypothesis test to determine if there is a a population difference in means between gallons received of substance XY-135 from Company A and Company B. Required:
What are your statistical hypotheses? What is your test statistic?