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. This type of test is used when the researcher is interested in determining if a particular characteristic or outcome exceeds a certain threshold or standard.

5 Must Know Facts For Your Next Test

1. In a right-tailed test, the null hypothesis is that the parameter is less than or equal to a specified value, while the alternative hypothesis states that the parameter is greater than that value.
2. The test statistic for a right-tailed test is compared to the critical value from the appropriate probability distribution, and the null hypothesis is rejected if the test statistic exceeds the critical value.
3. Right-tailed tests are commonly used in situations where the researcher wants to determine if a sample mean, proportion, or variance is significantly higher than a hypothesized value.
4. Examples of when a right-tailed test may be appropriate include testing if a new drug is more effective than a placebo, if a company's sales have increased compared to a previous year, or if a student's test score is above a certain threshold.
5. The choice of a right-tailed, left-tailed, or two-tailed test depends on the specific research question and the directionality of the alternative hypothesis.

Review Questions

• Explain how a right-tailed test is used in the context of hypothesis testing of a single mean.
  • In the context of hypothesis testing of a single mean, a right-tailed test is used when the researcher wants to determine if the population mean is greater than a specified value. The null hypothesis would state that the mean is less than or equal to the specified value, while the alternative hypothesis would state that the mean is greater than the specified value. The test statistic, such as the z-score or t-statistic, is compared to the critical value from the appropriate probability distribution, and the null hypothesis is rejected if the test statistic exceeds the critical value, providing evidence to support the alternative hypothesis.
• Describe how a right-tailed test is used in the context of hypothesis testing for two proportions.
  • When conducting a hypothesis test for two proportions, a right-tailed test can be used to determine if the proportion of successes in one population is significantly greater than the proportion of successes in another population. The null hypothesis would state that the two population proportions are equal, while the alternative hypothesis would state that the proportion in one population is greater than the proportion in the other population. The test statistic, such as the z-statistic, is compared to the critical value, and the null hypothesis is rejected if the test statistic exceeds the critical value, providing evidence to support the alternative hypothesis that the proportion in one population is significantly higher.
• Explain how a right-tailed test is used in the context of a goodness-of-fit test.
  • In a goodness-of-fit test, a right-tailed test can be used to determine if the observed frequencies in a sample are significantly different from the expected frequencies based on a hypothesized distribution. The null hypothesis would state that the observed frequencies follow the hypothesized distribution, while the alternative hypothesis would state that the observed frequencies are greater than the expected frequencies. The test statistic, such as the chi-square statistic, is compared to the critical value from the chi-square distribution, and the null hypothesis is rejected if the test statistic exceeds the critical value, providing evidence that the observed frequencies do not fit the hypothesized distribution.

Related terms

Hypothesis Testing: The process of using statistical analysis to determine whether a particular claim or hypothesis about a population parameter is likely to be true or false.

Null Hypothesis: The statement that there is no significant difference or relationship between the variables being studied, which the researcher aims to disprove.

Alternative Hypothesis: The statement that there is a significant difference or relationship between the variables being studied, which the researcher aims to provide evidence for.