## Five Steps in a Hypothesis Test

### Support or Reject Null Hypothesis

If H_{a} contains a less-than alternative, find the probability that is less than your test statistic (that is, look up your test statistic on the -table and find its corresponding probability). This is thevalue. (Note: In this case, your test statistic is usually negative.)

### How to Determine a p-Value When Testing a Null Hypothesis

Because this is a **two-sided alternative** hypothesis, the p-value is the combined area to the right of 2.47 and the left of −2.47 in a t-distribution with 35 – 1 = 34 degrees of freedom.

Remember that for something to be considered significant (leading us to reject null hypothesis) then the calculated Z score must be farther away from the mean than the critical value. We call the area past the critical value the rejection region. If any calculated ratio lands here, we reject the null hypothesis because our value is significantly different from the population. If it were to land before the critical value, we would fail to reject the null. In this case, because our sample mean is closer to the mean than the critical value, the correct decision is to __fail to reject the null__ hypothesis. Our sample was __not__ significantly different from the null hypothesized population of "no effect" due to the new wonder drug. In other words, the modest increase in IQ scores could be explained by chance variation and not necessarily due to the wonder drug.

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

**Sample question:** A researcher claims that more than 23% of community members go to church regularly. In a recent survey, 126 out of 420 people stated they went to church regularly. Is there enough evidence at α = 0.05 to support this claim? Use the P-Value method to support or reject null hypothesis.

## To find thevalue for your test statistic:

*Compare your answer from step 5 with the α value given in the question*. Support or reject the null hypothesis? If step 5 is less than α, reject the null hypothesis, otherwise do not reject it. In this case, .582 (5.82%) is not less than our α, so we do not reject the null hypothesis.

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

If H_{a} contains a greater-than alternative, find the probability that is greater than your test statistic (look up your test statistic on the -table, find its corresponding probability, and subtract it from one). The result is yourvalue. (Note: In this case, your test statistic is usually positive.)

## Support or Reject Null Hypothesis in Easy Steps

*Figure out the *. The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

## Null and Alternative Hypothesis | Real Statistics Using …

*State what will happen if the experiment doesn’t make any difference.* That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

## Journal of Articles in Support of the Null Hypothesis

The p-value is p = 0.236. This is not below the .05 standard, so we do not reject the null hypothesis. Thus it is possible that the true value of the population mean is 72. The 95% confidence interval suggests the mean could be anywhere between 67.78 and 73.06.