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MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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11. A one-tailed hypothesis test with the t statistic
Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for
remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial
tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with
antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children
with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions.
Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of disgust. The
average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to
be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion
recognition scale are normally distributed.
You believe that children with antisocial tendencies will have a harder time recognizing the emotion of disgust (in other words, they will have higher
scores on the emotion recognition test).
What is your null hypothesis stated using symbols? H,: Pantisocial S Hgeneral population ▼
What is your alternative hypothesis stated using symbols? H,: Mantisocial > Hgeneral population
This is a one-tailed test. Given what you know, you will evaluate this hypothesis using a t
Using the Distributions tool, locate the critical region for a = 0.05.
t Distribution
statistic.
Transcribed Image Text:11. A one-tailed hypothesis test with the t statistic Antisocial personality disorder (ASPD) is characterized by deceitfulness, reckless disregard for the well-being of others, a diminished capacity for remorse, superficial charm, thrill seeking, and poor behavioral control. ASPD is not normally diagnosed in children or adolescents, but antisocial tendencies can sometimes be recognized in childhood or early adolescence. James Blair and his colleagues have studied the ability of children with antisocial tendencies to recognize facial expressions that depict sadness, happiness, anger, disgust, fear, and surprise. They have found that children with antisocial tendencies have selective impairments, with significantly more difficulty recognizing fearful and sad expressions. Suppose you have a sample of 40 16-year-old children with antisocial tendencies and you are particularly interested in the emotion of disgust. The average 16-year-old has a score on the emotion recognition scale of 11.80. (The higher the score on this scale, the more strongly an emotion has to be displayed to be correctly identified. Therefore, higher scores indicate greater difficulty recognizing the emotion). Assume that scores on the emotion recognition scale are normally distributed. You believe that children with antisocial tendencies will have a harder time recognizing the emotion of disgust (in other words, they will have higher scores on the emotion recognition test). What is your null hypothesis stated using symbols? H,: Pantisocial S Hgeneral population ▼ What is your alternative hypothesis stated using symbols? H,: Mantisocial > Hgeneral population This is a one-tailed test. Given what you know, you will evaluate this hypothesis using a t Using the Distributions tool, locate the critical region for a = 0.05. t Distribution statistic.
t Distribution
Degrees of Freedom = 33
OOO
^^^
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
x
In order to use the t distribution, you will first need to determine the degrees of freedom (df) for a = 0.05. The degrees of freedom (df) is 39 ▼
The critical value of t is 1.685
Your sample of 16-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28.
The t statistic does not lie in the critical region. Therefore, you cannot reject the null hypothesis.
Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is 0.52. The t
statistic is 1.45 ▼ (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t
statistic.)
Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty
recognizing disgust than do children without antisocial tendencies.
Transcribed Image Text:t Distribution Degrees of Freedom = 33 OOO ^^^ -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 x In order to use the t distribution, you will first need to determine the degrees of freedom (df) for a = 0.05. The degrees of freedom (df) is 39 ▼ The critical value of t is 1.685 Your sample of 16-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28. The t statistic does not lie in the critical region. Therefore, you cannot reject the null hypothesis. Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is 0.52. The t statistic is 1.45 ▼ (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t statistic.) Based on the results of this test, there is not enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing disgust than do children without antisocial tendencies.
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