Answered: Construct a 90% confidence interval for…

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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The authors of a research article were interested in the effect on female viewers of watching movies in which female heroines were portrayed in roles that focus on their sex appeal. They carried out an experiment in which female college students were assigned at random to one of two experimental groups. The 24 women in one group watched 13 minutes of scenes from a certain superhero film series and then responded to a questionnaire designed to measure body esteem. Lower scores on this measure correspond to lower body satisfaction. The 29 women in the other group (the control group) did not watch any video prior to responding to the questionnaire measuring body esteem. For the women who watched the video, the mean body esteem score was 4.44 and the standard deviation was 1.02. For the women in the control group, the mean body esteem score was 5.07 and the standard deviation was 0.96. For purposes of this exercise, you may assume that the distribution of body esteem scores for each of the two treatments (video and control) is approximately normal.

(a)

Construct a 90% confidence interval for the difference in mean body esteem score for the video treatment and the no video treatment. (Use

?_video − ?_{no video}.

Use SALT. Round your answers to two decimal places.)

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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