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 a certain value. It is used when the researcher is interested in determining if a sample statistic is significantly larger than a hypothesized population parameter.

5 Must Know Facts For Your Next Test

1. In a right-tailed test, the null hypothesis (H₀) specifies that the parameter is less than or equal to a certain value, while the alternative hypothesis (H₁) specifies that the parameter is greater than that value.
2. The test statistic for a right-tailed test is compared to a critical value from the appropriate probability distribution, and the null hypothesis is rejected if the test statistic is greater than the critical value.
3. Right-tailed tests are commonly used in situations where the researcher is interested in determining if a sample mean, proportion, or other statistic is significantly larger than a hypothesized population parameter.
4. Examples of when a right-tailed test might be used 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 higher than a minimum passing score.
5. The choice of a right-tailed, left-tailed, or two-tailed test depends on the specific research question and the direction of the effect the researcher is interested in detecting.

Review Questions

• Explain how a right-tailed test is used in the context of hypothesis testing.
  • In a right-tailed test, the null hypothesis (H₀) specifies that the parameter of interest is less than or equal to a certain value, while the alternative hypothesis (H₁) specifies that the parameter is greater than that value. The test statistic is compared to a critical value from the appropriate probability distribution, and the null hypothesis is rejected if the test statistic is greater than the critical value. This type of test is used when the researcher is interested in determining if a sample statistic is significantly larger than a hypothesized population parameter.
• Describe how a right-tailed test would be used in the context of comparing two population means with known standard deviations.
  • When comparing two population means with known standard deviations, a right-tailed test could be used to determine if the mean of one population is significantly greater than the mean of the other population. The null hypothesis would be that the difference between the means is less than or equal to 0, while the alternative hypothesis would be that the difference is greater than 0. The test statistic, such as the z-score, would be calculated and compared to the critical value from the standard normal distribution. If the test statistic is greater than the critical value, the null hypothesis would be rejected, indicating that the mean of one population is significantly larger than the mean of the other population.
• Analyze how a right-tailed test would be applied in the context of a goodness-of-fit test, and explain the interpretation of the results.
  • In the context of a goodness-of-fit test, a right-tailed test could be used to determine if the observed frequencies in a sample are significantly greater than the expected frequencies based on a hypothesized probability distribution. The null hypothesis would be that the observed frequencies are less than or equal to the expected frequencies, while the alternative hypothesis would be that the observed frequencies are greater than the expected frequencies. The test statistic, such as the chi-square statistic, would be calculated and compared to the critical value from the chi-square distribution. If the test statistic is greater than the critical value, the null hypothesis would be rejected, indicating that the observed frequencies are significantly larger than the expected frequencies, and the hypothesized probability distribution does not adequately fit the observed data.

Related terms

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

Alternative Hypothesis: The statement that the parameter of interest is different from the value specified in the null hypothesis.

Test Statistic: A value calculated from sample data that is used to determine whether to reject or fail to reject the null hypothesis.