## Null hypothesis: μ = 72 Alternative hypothesis: μ ≠72

### What is the difference between confidence intervals and hypothesis ..

On the other hand, the null hypothesis is straightforward -- what is the probability that our treated and untreated samples are from the same population (that the treatment or predictor has no effect)? There is only one set of statistical probabilities -- calculation of chance effects. Instead of directly testing H, we test H. If we can reject H, (and factors are under control), we can accept H. To put it another way, the fate of the research hypothesis depends upon what happens to H.

### Understanding Hypothesis Tests: Confidence Intervals …

**NOTATION**: The notation *H*_{o} represents a null hypothesis and *H*_{a} represents an alternative hypothesis and p_{o} is read as p-not or p-zero and represents the null hypothesized value. Shortly, we will substitute μ_{o} for when discussing a test of means.

Note: In computing the Z-test statistic for a proportion we use the hypothesized value *p _{o}* here not the sample proportion p-hat in calculating the standard error! We do this because we "believe" the null hypothesis to be true until evidence says otherwise.

## a confidence interval or doing hypothesis ..

Let's see how we can use Minitab to calculate confidence intervals and conduct hypothesis tests for the slope *β*. Minitab's regression analysis output for our skin cancer mortality and latitude example appears below.

## Significance Testing and Confidence Intervals

In statistics, a *confidence interval* is an educated guess about some characteristic of the population. A confidence interval contains an initial estimate plus or minus a *margin of error* (the amount by which you expect your results to vary, if a different sample were taken). The following table shows formulas for the components of the most common confidence intervals and keys for when to use them.

## Confidence Intervals & Hypothesis Testing (2 of 5)

Third, we use the resulting test statistic to calculate the *P*-value. As always, the *P*-value is the answer to the question "how likely is it that we’d get a test statistic *t** as extreme as we did if the null hypothesis were true?" The *P*-value is determined by referring to a *t-*distribution with *n*-2 degrees of freedom.

## 3.3 Confidence Intervals and Hypothesis Testing …

Null hypothesis [written as H_{o}]: The two variables are **independent**.

Alternative hypothesis [written as H_{a}]: The two variables are **dependent**.

## Start studying 3.3 Confidence Intervals and Hypothesis ..

Because the *P*-value is so small (less than 0.001), we can reject the null hypothesis and conclude that *β* does not equal 0. There is sufficient evidence, at the α = 0.05 level, to conclude that there is a relationship in the population between skin cancer mortality and latitude.

## a hypothesis test or calculate a confidence interval

Third, we use the resulting test statistic to calculate the *P*-value. As always, the *P*-value is the answer to the question "how likely is it that we’d get a test statistic *t** as extreme as we did if the null hypothesis were true?" The *P*-value is determined by referring to a *t-*distribution with *n*-2 degrees of freedom.