Decreasing the alpha level from α = .05 to α = .01 ____.Group of answer choicesdecreases the probability of a Type I errorincreases the probability that the sample will fall into the critical regionincreases the size of the critical regionincreases the probability of a Type I error
Question
Decreasing the alpha level from α = .05 to α = .01 ____.Group of answer choicesdecreases the probability of a Type I errorincreases the probability that the sample will fall into the critical regionincreases the size of the critical regionincreases the probability of a Type I error
Solution
Decreasing the alpha level from α = .05 to α = .01 decreases the probability of a Type I error.
Here's why:
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The alpha level (α) is the threshold for determining when we reject the null hypothesis. If the p-value is less than or equal to α, we reject the null hypothesis.
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A Type I error occurs when we incorrectly reject the true null hypothesis. This means we believe there is a significant effect when there is not.
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By decreasing α from .05 to .01, we are making our threshold for rejecting the null hypothesis more stringent. This means it's harder to reject the null hypothesis, thus reducing the chance of making a Type I error.
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Therefore, decreasing α decreases the probability of a Type I error.
The other options are incorrect because:
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Decreasing α does not increase the probability that the sample will fall into the critical region. In fact, it makes it less likely because we are being more stringent about what we consider significant.
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Decreasing α does not increase the size of the critical region. The critical region is determined by α, so if α decreases, the critical region also decreases.
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Decreasing α does not increase the probability of a Type I error. As explained above, it decreases this probability.
Similar Questions
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Probability of a type I error
A manufacturer of electronic components claims that their production process produces resistors that are 90% defect-free.However, a customer suspects that the actual proportion of defective resistors may be much higher than that.To investigate this, a customer takes a random sample of 20 resistors from the manufacturer's production line and inspects them for defects.If three or more resistors are defective, the customer will not purchase the electronic components.Define the Null and Alternative Hypothesis;Define the Critical Value and Critical Region;Find the probability of committing a type I error assuming that manufacturer claim is True.Find the probability of committing a type II error for the alternative proportion of defected items of p=0.2.Hint: Use the Statistical Table A1 for the Binomial Probability Sums.
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