An engineer was investigating the relationship between the thrust of an experimental rocket (y), the percent composition of a secret chemical in the fuel (x1) and the internal temperature of a chamber of the rocket (x2). The engineer starts by fitting a quadratic model, but he believes that the full quadratic model is too complex and can be reduced by only including the linear terms and the interaction term.

The engineer obtained a random sample of 66 measurements and computed the SSE for both the complete model and the reduced model. The values were 1477.8 and 1678.8, respectively. Perform the appropriate test of hypothesis to determine whether the reduced model is adequate for the engineer's use. Use 0.05 significance level.