The Casamigos tequila company produces two different types of tequila, silver and gold. They want to see if people rate the two types differently. If they find a statistically significant difference between the two, they will be able to charge a higher price for the higher rated type of tequila. To test their claim, they conduct a focus group with 500 participants. Each of the participants were asked to rate the tequila on a scale from 1 to 10, with 1 being the worst and 10 being the best tequila they had ever had. Within the group, 275 of the participants were given the silver tequila, and 225 were given the gold tequila. Those who had the silver tequila rated it an average 9.49, while those who had the gold tequila rated it an average 9.17. The known population variance for silver tequila is 0.38 and for gold tequila it is 0.76. Let the silver tequila be population 1 and the gold tequila be population 2. Required:
Calculate the appropriate test statistic needed to test your claim.