# Hypothesis testing two sample case for the

Early use[ edit ] While hypothesis testing was popularized early in the 20th century, early forms were used in the s. Based on whether it is true or not determines whether we accept or reject the hypothesis. We accept true hypotheses and reject false hypotheses. The null hypothesis is the hypothesis that is claimed and that we will test against.

The alternative hypothesis is the hypothesis that we believe it actually is. For example, let's say that a company claims it only receives 20 consumer complaints on average a year. However, we believe that most likely it receives much more.

So when we do our testing, we see which hypothesis is actually true, the null claimed or the alternative what we believe it is. The significance level that you select will determine how broad of an area the rejection area will be. The significance level represents the total rejection area of a normal standard curve.

The more you increase the significance level, the greater area of rejection there is. This means that there is a greater chance a hypothesis will be rejected and a narrower chance you have of accepting the hypothesis, since the nonrejection area decreases.

So the greater the significance level, the smaller or narrower the nonrejection area.

## Introduction to Hypothesis Testing

The smaller the significance level, the greater the nonrejection area. There are 3 types of hypothesis testing that we can do. There is left tail, right tail, and two tail hypothesis testing. Left Tail Left tail hypothesis testing is illustrated below: We use left tail hypothesis testing to see if the z score is above the significance level critical value, in which case we cannot reject the hypothesis.

The left tail method, just like the right tail, has a cutoff point. The significance level that you choose determines this cutoff point called the critical value.

Any value below this critical value in the left tail method represents the rejection area. This means that if we obtain a z score below the critical value, the z score will be in the rejection area.

This means that the hypothesis is false. If the z score is above the critical value, this means that it is is in the nonrejection area, and we cannot reject the hypothesis. The left tail method is used if we want to determine if a sample mean is less than the hypothesis mean.

If the z score is below the critical value, this means that we reject the hypothesis, because the hypothesis mean is much higher than what the real mean really is. Therefore, it is false and we reject the hypothesis.

In this case, the alternative hypothesis is true. If the z score is above the critical value, this means that we cannot reject the null hypothesis and we reject the alternative hypothesis which states it is less, because the real mean is really greater than the hypothesis mean.

Right Tail Right tail hypothesis testing is illustrated below: We use right tail hypothesis testing to see if the z score is below the significance level critical value, in which case we cannot reject the null hypothesis as true. The right tail method, just like the left tail, has a critical value. The significance level that you choose determines this critical value point.Introduction. Author(s) David M. Lane Prerequisites. Causation, Binomial Distribution Learning Objectives.

Describe the logic by which it can be concluded that someone can distinguish between two . Encyclopedia of Business, 2nd ed. Hypothesis Testing: Gr-Int.

In this case, for type of major, the p-value for the two-sample t-test was , which is not significant at the 95% confidence level (α=). Therefore, the class would fail to reject the null hypothesis and conclude that there is no significant difference between the two population means. • Explain the logic of hypothesis testing, as applied to the two-sample case • Perform a test of hypothesis for two sample means or two sample proportions, following the five-step model and correctly interpret the results • List and explain each of the factors (especially sample. Hypothesis Testing: Two-Sample Case for the Mean Many cases in the social sciences involve a hypothesis about the difference between two groups (i.e. men and women, control and experiment). We analyze statistics from two samples, and the hypothesis and confidence interval would deal with the difference between two population means.

Social science research, and by extension business research, uses a number of different approaches to study a variety of issues. Hypothesis Testing: Two sample means Lesson Overview. Unmatched (independent) Two-sample t Test; we do use the t distribution for hypothesis testing in this case.

## One-Tail vs Two-Tail Testing (Does it Matter?)

The two-sample t statistic is as follows: this latter procedure also becomes more accurate. The two-sample t procedures are more robust than the one-sample methods.

The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. Test Statistics The stats program works out the p value either directly for the statistic you're interested in (e.g.

a correlation), or for a test statistic that has a relationship with the effect statistic.A test statistic is just another kind of effect statistic, one that is easier for statisticians and computers to handle.

Common test statistics are t, F, and chi-squared. Summary. One of the main goals of statistical hypothesis testing is to estimate the P value, which is the probability of obtaining the observed results, or something more extreme, if the null hypothesis were true.

If the observed results are unlikely under the null hypothesis, your reject the null hypothesis. New View of Statistics: P Values