In a study on the effectiveness of the Montessori method in preschool education, 54 three-year-olds were assigned to Montessori preschools, and 112 three-year-olds were assigned to other preschools. Two years later, parents of 30 of the Montessori children and 25 of the others agreed to participate in follow-up testing. On a math assessment, the Montessori group had an average score of 19 and a standard deviation of 3.11, and the other group had an average score of 17 and a standard deviation of 4.19. We want to use a two-sample t-test to decide if this is statistically significant evidence of a difference between the two populations means.

What is the conservative estimate for the number of degrees of freedom?

In Table C, find the critical value t* for a two-sided P-value of .05 with that many degrees of freedom.

Find the standard error. Give your answer to two decimal places.

Find the t-statistic. Give your answer to two decimal places.

Is this statistically significant evidence of a difference? Answer yes or no.