1. Consider a dataset of two paired variables, X and Y, that have the following properties

n=8    x>y      Sy>0       SEd=0

a. Provide values for x and y that have the four properties listed above. there are many possible solutions, so be sure to show that each of these properties is true.

b. Suppose this data met all assumptions of a paired t-test. Why would you still be unable to test if there is a significant mean difference?

2. To investigate if autism is marked by different brain growth parents in early life, studies have tried to link brain size in infants and toddlers to autism. Suppose the whole-brain volume in non-autisitic toddlers is known to be 1200 milliliters, on average. One study based on a sample size of 35 estimated the mean whole-brain volume in autistic toddlers with a 95% confidence interval of [1220ml, 1400ml].

a. Do the results from this study suggest that autistic toddlers have the same whole-brain volume on average?

b. If you used the same data from this study and calculated a 90% confidence interval, would it be wider or narrower than the 95% interval?

c. If the data from this study had the same mean and SD, but was from a sample size of 70 instead of 35, would the 95% confidence have been wider or narrower?