2 Is autism marked by different brain growth patterns in ear

2. Is autism marked by different brain growth patterns in early life, even before a diagnosis of
autism is made? Studies have linked brain size in infants and toddlers to a number of ailments,
including autism. Suppose the whole-brain volume in non-autistic toddlers is known to be 1200
milliliters, on average. One study found the 95% confidence interval for the average whole-brain volume in autistic toddlers to be [1220 ml, 1400 ml].

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

volume, on average? Justify your answer. (1pt)

b. If you conducted a t test with significance level = 0.05, would you reject or fail to reject
the null hypothesis that autistic toddlers have the same whole-brain volume, on average?

(1pt)
c. Suppose you conducted a t test with significance level = 0.10. Do you have sufficient
information to conclude whether you would reject or fail to reject the null hypothesis that
autistic toddlers have the same whole-brain volume, on average? If so, what would you

conclude? (2pt)

3. Researchers tested 150 farm-raised salmon for organic contaminants. They found the mean
concentration of the carcinogenic insecticide mirex to be 0.09 ppm (parts per million), with
standard deviation 0.05 ppm. As a safety recommendation to recreational fishers, the EPA’s
recommended “screening value” for mirex is 0.08 ppm.a. Are farm-raised salmon contaminated more than the level recommended by the EPA?

Assuming that the concentration of mirex in salmon is normally distributed, conduct a
hypothesis test to answer this question, including all necessary steps. (6 pt)

b. State in words how you can make a Type I error for this problem. What can you do to
reduce the chance of such an error? (2 pt)

c. State in words how you can make a Type II error for this problem. What can you do to
reduce the chance of such an error? (2 pt)d. Suppose this study were based on a sample of 100 salmon instead of 150, would the p-value be smaller, larger or the same? (2 pt)

Solution

2. Is autism marked by different brain growth patterns in early life, even before a diagnosis of
autism is made? Studies have linked brain size in infants and toddlers to a number of ailments,
including autism. Suppose the whole-brain volume in non-autistic toddlers is known to be 1200
milliliters, on average. One study found the 95% confidence interval for the average whole-brain volume in autistic toddlers to be [1220 ml, 1400 ml].

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a. Do the results from this study suggest that autistic toddlers have the same whole-brain
volume, on average? Justify your answer. (1pt)

Yes, as 1200 is not part of the confidence interval for those with autism.

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b. If you conducted a t test with significance level = 0.05, would you reject or fail to reject
the null hypothesis that autistic toddlers have the same whole-brain volume, on average?
(1pt)

WE WILL REJECT THE NULL HYPOTHESIS, as 1200 mL is not on the 95% confidence interval.

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c. Suppose you conducted a t test with significance level = 0.10. Do you have sufficient
information to conclude whether you would reject or fail to reject the null hypothesis that
autistic toddlers have the same whole-brain volume, on average? If so, what would you
conclude? (2pt)

If we reject at 0.05 level, then most surely we will reject all the more at 0.10 level, as 0.05 level is even stricter.

So, WE REJECT THE NULL HYPOTHESIS AT 0.10 LEVEL, and we conclude that ther is a significant difference between the whole-brain volume of non-autistic toddlers to the autistic toddlers. [answer]

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