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To investigate if autism is marked by different brain growth patterns in early life, studies have tried to link brain size in infants and toddlers to autism. Suppose the whole-brain volume in non-autistic toddlers is known to be 1200 milliliters, on average. One study based on a sample size of 25 autistic toddlers had a sample mean volume of 1280 ml with a standard deviation of 230 ml. a. Calculate a 95% confidence interval for the whole-brain volume of autistic toddlers. Given: �!"!!" ∗ = 2.064

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Answer:

95% confidence interval for the whole-brain volume of autistic toddlers is between a lower limit of 1185.056 ml and an upper limit of 1374.944 ml.

Explanation:

Confidence interval = mean + or - Error margin (E)

mean = 1280 ml

sd = 230 ml

n = 25

degree of freedom = n - 1 = 25 - 1 = 24

confidence level = 95%

t-value corresponding to 24 degrees of freedom and 95% confidence level is 2.064

E = t×sd/√n = 2.064×230/√25 = 94.944 ml

Lower limit = mean - E = 1280 - 94.944 = 1185.056 ml

Upper limit = mean + E = 1280 + 94.944 = 1374.944 ml

95% confidence interval is between 1185.056 ml and 1374.944 ml.

The 95% confidence interval for the whole-brain volume of autistic toddlers is between a lower limit of 1185.056 ml and an upper limit of 1374.944 ml.

Calculation of the 95% confidence interval:

Here we know that

Confidence interval = mean + or - Error margin (E)

Here,

mean = 1280 ml

sd = 230 ml

n = 25

Now

degree of freedom = n - 1 = 25 - 1 = 24

So,

E = t×sd/√n = 2.064×230/√25 = 94.944 ml

Now

Lower limit = mean - E = 1280 - 94.944 = 1185.056 ml

Upper limit = mean + E = 1280 + 94.944 = 1374.944 ml

Learn more about sample here: https://brainly.com/question/20278279

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