Avoid rounding until you compute the CI-test(s). When you compute the CI-test(s), round to 4 decimal places. Researchers studied the effectiveness of learning about a new medication. One group of participants (n = 12) read a short paragraph describing the medication, while another group (n = 12) read the same paragraph but were also provided with a graph that depicted the data that they had read about. Both groups were asked to rate their perceived effectiveness of the medication. The reading only group had a mean of 6.25 (SS=28.25) and the reading-plus-graph group had a mean of 6.83 (SS=15.67). The researchers now want to use estimation procedures to draw conclusions about whether the perceived drug effectiveness differs between the two groups. For the procedures below think very carefully about the design of the study and what this means for the type of test you should use. Also pay close attention to which point estimate, df, and standard error formulas that should be used. 1. What is the correct formula for this type of design? 2. Compute the point estimate. 3. Compute the 80% confidence interval around the mean difference. Be sure to state your results in statistical notation. 4. Compute the 95% confidence interval around the mean difference. Be sure to state your results in statistical notation.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Avoid rounding until you compute the CI-test(s). When you compute the CI-test(s), round to 4 decimal places.

Researchers studied the effectiveness of learning about a new medication. One group of participants (n = 12) read a short paragraph describing the medication, while another group (n = 12) read the same paragraph but were also provided with a graph that depicted the data that they had read about. Both groups were asked to rate their perceived effectiveness of the medication. The reading only group had a mean of 6.25 (SS=28.25) and the reading-plus-graph group had a mean of 6.83 (SS=15.67). The researchers now want to use estimation procedures to draw conclusions about whether the perceived drug effectiveness differs between the two groups. For the procedures below think very carefully about the design of the study and what this means for the type of test you should use. Also pay close attention to which point estimate, df, and standard error formulas that should be used.

1. What is the correct formula for this type of design?

2. Compute the point estimate.

3. Compute the 80% confidence interval around the mean difference. Be sure to state your results in statistical notation.

4. Compute the 95% confidence interval around the mean difference. Be sure to state your results in statistical notation.

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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