On the previous midterm, we investigated scores on the Wechsler Intelligence Scale for Children (WISC). Scores in neurotypical children have population mean 100 and population standard deviation 15. For a sample of 49 autistic children, the mean score was 94.6. Assume the population standard deviation is the same in neurotypical and autistic children. A) Test whether the mean WISC score of autistic children is below 10°. Use a 1% significance level. What do you conclude about the mean score of autistic children compared to neurotypical children? B) If we used a 5% significance level instead, which of the following would change? Circle all correct answers (one or more) below. null hypothesis test statistic value p-value z critical value C)lf we had a sample of 100 children instead, which of the following would change? Circle all correct answers (one or more) below. null hypothesis test statistic value p-value z critical value D) What is the power of this test to detect the specific alternative μ-95, that is, that the population mean WISC score of autistic children is 5 points less than that of neurotypical children? (Keep the original 1% significance level and sample size of 49 children) E) Based on your answer to part D (make up a value if you need to), is a sample of 49 children sufficiently large to detect this alternative? Why or why not? F) What is the probability of Type 1 Error for this test? G) What is the probability of Type II Error for this test?

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