In order to use the t distribution, you will first need to determine the degrees of freedom (df) for a = .05. The degrees of freedom (df) The critical value of t is Your sample of 10-year-old children with antisocial tendencies has an average score of 14.35 with a standard deviation of 4.63. 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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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