In order to use thet distribution, you will first need to determine the degrees of freedom (df) for a = 0.05. The degrees of freedom (df) is critical value of t is The Your sample of 12-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28. Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is_▼ . The t statistic is . (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t statistic.) The t statistic lie in the critical region. Therefore, you reject the null hypothesis. Based on the results of this test, there enough evidence to conclude that children with antisocial tendencies have greater difficulty recognizing sadness than do children without antisocial tendencies.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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![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
The
critical value of t is
Your sample of 12-year-old children with antisocial tendencies has an average score of 12.55 with a standard deviation of 3.28.
Calculate the t statistic. To do this, you will first have to calculate the estimated standard error. The estimated standard error is
. (Hint: For the most precise results, retain four significant figures from your calculation of the standard error to calculate the t statistic.)
Z . The t statistic is
The t statistic
lie in the critical region. Therefore, you
reject the null hypothesis.
Based on the results of this test, there
enough evidence to conclude that children with antisocial tendencies have greater difficulty
recognizing sadness than do children without antisocial tendencies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ffcf077-dbb8-4bb8-8db9-7ad786a42303%2F3f000687-65d4-429f-856c-83e59ebfd158%2Fe4ng05h_processed.png&w=3840&q=75)
![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 12-year-old children with antisocial tendencies and you are particularly interested in the emotion of sadness. The
average 12-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 sadness (in other words, they will have higher
scores on the emotion recognition test).
What is your null hypothesis stated using symbols?
Ho: Hantinocial = Hgeneral population
What is your alternative hypothesis stated using symbols?
H1: Hantisocial + Pgeneral population
This is a one-
tailed test. Given what you know, you will evaluate this hypothesis using a
statistic.
Using the Distributions tool, locate the critical region for a = 0.05.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ffcf077-dbb8-4bb8-8db9-7ad786a42303%2F3f000687-65d4-429f-856c-83e59ebfd158%2Fl94fktc_processed.png&w=3840&q=75)
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