Chapter 6, Section 2-HT, Exercise 121 - MathPad The Autistic Brain Autistic children often have a small head circumference at birth, followed by a sudden and excessive increase in head circumference during the first year of life. A recent study1 examined the brain tissue in autopsies of seven autistic male children between the ages of 2 and 16. The mean number of neurons in the prefrontal cortex in non-autistic male children of the same age is about 1.15 billion. The prefrontal cortex is the part of the brain most disrupted in autism, as it deals with language and social communication. In the sample of seven autistic children, the mean number of neurons in the prefrontal cortex was 1.94 billion with a standard deviation of 0.50 billion. The values in the sample are not heavily skewed. Use the t-distribution to test whether this sample provides evidence that autisticmale children have more neurons (on average) in the prefrontal cortex than non-autistic children. (This study indicates that the causes of autism may be present before birth.) 1Adapted from Courchesne,E., et.al., ‘‘Neuron Number and Size in Prefrontal Cortex of Children with Autism,” Journal of the American Medical Association, November 2011; 306(18): 2001-2010. Incorrect. State the null and alternative hypotheses. Your answer should be an expression composed of symbols: =,≠,<,>,μ,μ1,μ2,p,p1,p2,1.15,ρ,p^,p^1,p^2,r. H0:μ=1.5 vs Ha:μ≠1.5Edit SHOW HINT LINK TO TEXT Correct. Give the test statistic and the p-value and state the conclusion of the test. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places. test statistic = Enter your answer; test statistic p-value = Enter your answer; p-value Conclusion: Choose the answer from the menu; Conclusion H0. SHOW HINT SHOW SOLUTION SHOW ANSWER LINK TO TEXT Correct. Does the sample provide evidence that autistic male children have more neurons (on average) in the prefrontal cortex than non-autistic children? Yes No
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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