Right-Tailed Test

Definition

A right-tailed test is a statistical hypothesis test where the alternative hypothesis specifies that the parameter of interest is greater than the value stated in the null hypothesis. It is used to determine if there is sufficient evidence to conclude that the true value of the parameter exceeds a particular threshold.

5 Must Know Facts For Your Next Test

1. In a right-tailed test, the alternative hypothesis is that the parameter of interest is greater than the value specified in the null hypothesis.
2. The test statistic for a right-tailed test falls in the right-hand side of the sampling distribution under the null hypothesis.
3. The p-value in a right-tailed test represents the probability of observing a test statistic greater than or equal to the calculated value, given that the null hypothesis is true.
4. Right-tailed tests are commonly used when the research hypothesis suggests that the parameter of interest has increased or is greater than a specified value.
5. The decision to reject the null hypothesis in a right-tailed test is made when the p-value is less than the chosen significance level, indicating strong evidence to support the alternative hypothesis.

Review Questions

• Explain how a right-tailed test is used in the context of the Central Limit Theorem for Sample Means.
  • In the context of the Central Limit Theorem for Sample Means, a right-tailed test can be used to determine if the true population mean is greater than a specified value. The null hypothesis would state that the population mean is equal to the specified value, while the alternative hypothesis would state that the population mean is greater than the specified value. If the test statistic falls in the right-hand side of the sampling distribution under the null hypothesis, and the p-value is less than the chosen significance level, the researcher can reject the null hypothesis and conclude that the population mean is greater than the specified value.
• Describe how a right-tailed test is used when comparing two independent population means.
  • When comparing two independent population means, a right-tailed test can be used to determine if the true difference between the means is greater than a specified value. The null hypothesis would state that the difference between the population means is equal to the specified value, while the alternative hypothesis would state that the difference is greater than the specified value. If the test statistic falls in the right-hand side of the sampling distribution under the null hypothesis, and the p-value is less than the chosen significance level, the researcher can reject the null hypothesis and conclude that the difference between the population means is greater than the specified value.
• Explain the use of a right-tailed test in the context of comparing two independent population proportions.
  • In the context of comparing two independent population proportions, a right-tailed test can be used to determine if the true difference between the proportions is greater than a specified value. The null hypothesis would state that the difference between the population proportions is equal to the specified value, while the alternative hypothesis would state that the difference is greater than the specified value. If the test statistic falls in the right-hand side of the sampling distribution under the null hypothesis, and the p-value is less than the chosen significance level, the researcher can reject the null hypothesis and conclude that the difference between the population proportions is greater than the specified value.

Related terms

Null Hypothesis:

The default or initial hypothesis that states there is no significant difference or relationship between the variables being studied.

Alternative Hypothesis:

The hypothesis that contradicts the null hypothesis and states that there is a significant difference or relationship between the variables.

p-value:

The probability of obtaining a test statistic at least as extreme as the one observed, given that the null hypothesis is true.