Question

The 95% confidence interval is functionally equivalent to:

A) non-directional hypothesis testing with a 0.05 alpha level.

B) an interval based on a directional test with a 2.5% chance of Type I Error.

C) the acceptable amount of Type I Error.

D) an inferential test with a 5% chance of Type II Error.

E) the likelihood of rejecting a false null 2.5% of the time.

Answer #1

**Solution:**

**The 95% confidence interval is functionally equivalent
to A) non-directional hypothesis testing with a 0.05 alpha
level.**

**Explanation:**

The 95% confidence interval means If repeated samples were taken and the 95% confidence interval was computed for each sample, 95% of the intervals would contain the population mean.

So, non-directional hypothesis testing is two-tailed test where we reject the null hypothesis for both the left and right side. If the value of the test statistics lies extreme to the distribution of the test statistics we reject the null. So, we reject the null left side with probability 0.025 and reject the null right side with probability 0.025. So, we reject the null in both directions with probability ( 0.025+0.025) = 0.05. We know the maximum permissible probability of rejecting the null hypothesis is the level of the test. So, the level of the test is 0.05.

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False
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failing to reject the null hypothesis when it is false.
rejecting the null hypothesis when it is true.
rejecting the null hypothesis when it is false.
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