A two-sample t-test was conducted at the 𝛼 = 0.01 level of significance to determine if full scale IQ differs between children whose blood-lead levels 40 mg/100ml. What is the probability of committing a Type I error?

Question

A two-sample t-test was conducted at the 
𝛼
=
0.01
 level of significance to determine if full scale IQ differs between children whose blood-lead levels <40 mg/100ml and children whose blood-lead levels > 40 mg/100ml.

What is the probability of committing a Type I error?

BlackTom AI · Accepted Answer

Starting with the concept at hand, the probability of committing a Type I error is defined by the significance level alpha set for the test.
Option 1: 0.1787 is the p-value from the test result or a random statistic, not the probability of a Type I error. It does not represent alpha.
Option 2: 0 is incorrect because the question specifies alpha = 0.01; a Type I error probability equal to zero would imply a perfect test, which is not the case here.
Option 3: 0.01 matches the stated significance level alpha. By definition, if the null hypothesis is true, the probability of rejecting it (a false positive) is controlled at alpha, here 1%. This is the Type I error rate the test is willing to tolerate.
Option 4: Not enough information to determine would be applicable if alpha were unspecified or if the question relied on additional context beyond the stated level of significance. Since alpha is clearly given as 0.01, this option is not appropriate.
Option 5: 0.05 would correspond to a different conventional threshold for significance, but the problem explicitly uses 0.01, so this value does not describe the Type I error probability for this test.

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A two-sample t-test was conducted at the 𝛼 = 0.01 level of significance to determine if full scale IQ differs between children whose blood-lead levels <40 mg/100ml and children whose blood-lead levels > 40 mg/100ml. What is the probability of committing a Type I error?

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