A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. What should the researcher’s conclusion be for a 5% significance level? A) We reject H0 at the 5% level because -57.53 is less than -1.96. We do have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%. B) We fail to reject H0 at the 5% because 1.12 is less than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%. C) We fail to reject H0 at the 5% because 1.09 is less than 1.96. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%. D) We fail to reject H0 at the 5% because 1.12 is greater than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
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!
A researcher suspects that the actual prevalence of generalized anxiety among children and adolescents is higher than the previously reported prevalence of generalized anxiety disorder among children and adolescents. The previously reported prevalence of generalized anxiety disorder among children and adolescents is 3.9%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of generalized anxiety disorder by recruiting 98 children and adolescents from various pediatricians’ offices and tests them for generalized anxiety disorder using the DSM-5. The researcher determines that the prevalence of generalized anxiety disorder among the participants of the study is 6.1%. What should the researcher’s conclusion be for a 5% significance level?
A) We reject H0 at the 5% level because -57.53 is less than -1.96. We do have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
B) We fail to reject H0 at the 5% because 1.12 is less than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
C) We fail to reject H0 at the 5% because 1.09 is less than 1.96. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
D) We fail to reject H0 at the 5% because 1.12 is greater than 1.645. We do not have statistically significant evidence to show the actual prevalence of generalized anxiety disorder among children and adolescents is above the previously reported prevalence of 3.9%.
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