The other factor affecting the critical t-value(s) is whether thealternative hypothesis is one- or two-tailed (see Hypothesis Testingtutorial for review of one-tailed and two-tailed hypotheses).

He or she could have stated the alternative hypothesis as thefollowing directional hypothesis: Students at State University aresatisfied with dormitory living.

Following the above process for this test, the K-S statistic is 0.421 with the p-value of 0.0009, indicating a strong evidence against the null hypothesis.

The p-value is equal to 0.062, indicating that there is moderate evidence against the null hypothesis that the three populations are statistically identical.

Using the JavaScripts, we obtain the needed information in constructing the following ANOVA table: **Conclusion:** The p-value is P= 0.006, indicating a strong evidence against the null hypothesis.

In many statistical tests, you’ll want to either reject or support the . For elementary statistics students, the term can be a tricky term to grasp, partly because the name “null hypothesis” doesn’t make it clear about *what *the null hypothesis actually is!

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The null hypothesis can be thought of as a *nullifiable *hypothesis. That means you can nullify it, or reject it. What happens if you reject the null hypothesis? It gets replaced with the which is what you think might actually be true about a situation. For example, let’s say you think that a certain drug might be responsible for a spate of recent heart attacks. The drug company thinks the drug is safe. The null hypothesis is always the accepted hypothesis; in this example, the drug is on the market, people are using it, and it’s generally accepted to be safe. Therefore, the null hypothesis is that the drug is safe. The alternate hypothesis — the one you want to replace the null hypothesis, is that the drug *isn’t* safe. Rejecting the null hypothesis in this case means that you will have to prove that the drug is not safe.

When drawing conclusions about a population from randomly chosen samples (a process called ), you can use two methods: confidence intervals and hypothesis testing.

A is a range of values that’s expected to contain the value of a population parameter with a specified level of confidence (such as 90 percent, 95 percent, 99 percent, and so on). For example, you can construct a confidence interval for the population mean by following these steps:

**State the null hypothesis.** When you state the null hypothesis, you also have to state the alternate hypothesis. Sometimes it is easier to state the alternate hypothesis first, because that’s the researcher’s thoughts about the experiment. (opens in a new window).

When we were constructing confidence intervals, it mattered whether the data were drawn from normally distributed populations, whether the population standard deviations were equal, and whether the sample sizes were large or small, The answers to these questions helped us determine the proper multiplier for the standard error. The same considerations apply to significance tests. The answers determine the critical value of for a result to be declared statistically significant.

The margin of error depends on the size of the sample used to construct the confidence interval, whether the population standard deviation is known, and the level of confidence chosen.

Theconfidence interval includes all null hypothesis values for thepopulation mean that would be accepted by an hypothesis test at the5 % significance level.

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