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The significance level is 5%. the p-value was 0.014. what is the probability of a type i error for this hypothesis test (assuming that the null hypothesis is true)? group of answer choices 0.05 0.014 it is impossible to tell from the information given.

User Stenix
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Final answer:

The probability of a Type I error in a hypothesis test is fixed by the significance level set for the test. In this case, since the significance level is 5%, the probability of committing a Type I error is also 5%, regardless of the p-value.

Step-by-step explanation:

The question revolves around the concept of hypothesis testing in statistics, with specific reference to the significance level, p-value, and Type I error. The significance level, often represented as α (alpha), is the threshold below which we reject the null hypothesis.

In this case, the significance level is 5% or 0.05. A p-value is the probability of obtaining a sample result as extreme as the one observed, under the assumption that the null hypothesis is true. If the p-value is less than alpha, we reject the null hypothesis.

Regarding the possibility of a Type I error, which is the incorrect rejection of a true null hypothesis, this probability is fixed by the significance level set before testing begins. Therefore, the probability of a Type I error for this hypothesis test is the significance level itself, which is 0.05 or 5%.

In the given scenario, the p-value is 0.014, which is smaller than the significance level of 0.05. As per the conventional criteria, this would lead to a decision to reject the null hypothesis. Nonetheless, the probability of a Type I error is not equal to the p-value but is determined by the preset significance level. Hence, the correct answer to the question is 0.05, representing the fixed probability of committing a Type I error when the null hypothesis is in fact true.

User Jaspero
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