The flatwise bonding strength (in lb/in.) of dowel joints of two different types was determined for two random samples of joints of each of the two types: "Thin rail" and "Thick rail". The summary is below:
Sample size Sample mean Sample standard deviation
Thin rail 13 1243.8 147.3
Thick rail 9 1411.3 166.4
At 5% significance level, does the type of dowel with the thicker rail have a greater true average bonding strength than the type with the thinner rail? Assume that the bonding strengths are normally distributed.