# Any confidence interval has a hypothesis test dual to it.

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A confidence interval (CI) consists of the possible values that cannot be rejected of a hypothesis test whose 0 is that ``the value of the observed sample statistic corresponds exactly to the population value it estimates''.

## Identify the null and alternativehypothesis.

### the null hypothesis is rejected when it is true b.

Now that we have reviewed the critical value and P-value approach procedures for each of three possible hypotheses, let's look at three new examples — one of a right-tailed test, one of a left-tailed test, and one of a two-tailed test.

### the null hypothesis is not rejected when it is false c.

The good news is that, whenever possible, we will take advantage of the test statistics and P-values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

## the null hypothesis is rejected when it is true.

Because,whether parametric or nonparametric and whether done analytically or bysimulation, the reference distribution for a hypothesis test mustbe a distribution satisfying the null hypothesis.

## The failure to reject does not imply the null hypothesis is true.

Then one would, for example, comparethe value of the sample mean with that of the population mean and if thedifference is small, then one would accept that both are the same or thatThe null hypothesis is not rejected (almost saying that its istrue) or .

## Confidence Intervals & Hypothesis Testing (1 of 5)

Know how much the difference in comparing both means will be in orderto reject the null hypothesis (that both means are not the same) is a matterof probability or how confident or certain you want to be in making thatjudgment.

## 95% confidence intervals and the null hypothesis

(How else can it be relevantto the null hypothesis?)A naive person attempting to do a bootstrap test just calculates a-value as something likewhere is the value of the test statistic calculatedfor the actual data and is a vector of values ofthe test statistic calculated for bootstrap samples.

### failing to reject the null hypothesis when it is false.

Bugbee - UNH True/FalseTESTOFSIGNIFICAN TYPE1ERROR CONFIDENCEINTERV CONCEPT STATISTICS ESTIMATIONT= 2 ComprehensionD= 1 GeneralBack to 1661-4

### rejecting the null hypothesis when it is true.

In hypothesis testing we present this view of deciding on a level ofacceptance of the null hypothesis: If there is a low probability that wecan reject the null hypothesis, then we say that the null hypothesis "istrue."
This low probability of rejecting the null hypothesis is called thesignificantlevel, and is called alpha or denoted by the symbol,or .

### rejecting the null hypothesis when the alternative is true.

In acceptingthe alternate hypothesis one rejects the null hypothesis and in acceptingthe alternate hypothesis, one rejects the null hypothesis.