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 of12children who were tutored using Method A and10children who were tutored using Method B were chosen at random. The Method A children took a mean of35minutes to solve a certain puzzle with a standard deviation of6minutes. The Method B children took a mean of33minutes to solve the same puzzle with a standard deviation of8minutes. Assume that the two populations of completion times are normally distributed and that the population variances are equal. Construct a99%confidence interval for the difference−μ1μ2between 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 the99%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.)

Denote μ1, μ2 as the population mean times to solve puzzle using Method A and B, respectively

Answered: An educational psychologist is studying…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 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.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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