An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of 12 children who were tutored using Method A and 10 children who were tutored using Method B were chosen at random. The Method A children took a mean of 35 minutes to solve a certain puzzle with a standard deviation of 6 minutes. The Method B children took a mean of 33 minutes to solve the same puzzle with a standard deviation of 8 minutes. Assume that the two populations of completion times are normally distributed and that the population variances are equal. Construct a 99% confidence interval for the difference −μ1μ2 between the mean puzzle-solving times for Method A children ( μ1 ) and for Method B children ( μ2 ). Then find the lower limit and upper limit of the 99% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)
An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of
children who were tutored using Method A and
children who were tutored using Method B were chosen at random. The Method A children took a mean of
minutes to solve a certain puzzle with a standard deviation of
minutes. The Method B children took a mean of
minutes to solve the same puzzle with a standard deviation of
minutes. Assume that the two populations of completion times are
confidence interval for the difference
between the mean puzzle-solving times for Method A children (
) and for Method B children (
). Then find the lower limit and upper limit of the
confidence interval.
Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal places. (If necessary, consult a list of formulas.)
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