Discuss how a t Test can be employed in hypothesis testing by the use of directional vs. non directional hypotheses. Discuss types of research where using the t statistic may be an appropriate alternative to using a z-score.
Usually you use z-tests when sample sizes are large (n is greater than
or equal to 30) whether or not you know the population standard deviation.
If you do not know the population standard deviation and have a small
sample (n < 30), then you can use t-tests.
The alternate or alternative hypothesis tells you whether or not the test is directional or nondirectional. If the alternate hypothesis uses "greater than" or "less than" symbols, the test is directional. If the alternate hypothesis uses "does not equal" in its statement, then the test is nondirectional.
I hope these few hints will help.
The computed t was -.926 with df of 24 for p>.o5. what may you say about the null hypothesis?
THE f-RATIO WAS 2.293 WITH DF OF (12,8)) FOR P>.05. What may you say about the alternate hypothesis.
I would say the alternate hypothesis is rejected
In hypothesis testing, a t-test is a statistical method used to compare two sample means and determine if there is a significant difference between them. The t-test is applicable when the population standard deviation is unknown and must be estimated using sample data. It is a versatile tool that can be employed in various research scenarios.
Directional versus non-directional hypotheses:
When conducting a hypothesis test, researchers typically formulate a null hypothesis (H0) and an alternative hypothesis (Ha). The alternative hypothesis can be directional or non-directional.
1. Directional hypothesis: This type of hypothesis predicts the direction of the difference between the two sample means. For example, "Group A will have a higher mean score than Group B" or "The new treatment will decrease the mean response time." In this case, a one-tailed t-test is used to determine if the observed difference is statistically significant in the specified direction.
2. Non-directional hypothesis: This type of hypothesis does not predict any specific direction of the difference between the means. For example, "There will be a difference in mean scores between Group A and Group B" or "The new treatment will lead to a change in response time." In this case, a two-tailed t-test is used to determine if there is a significant difference in either direction.
Research scenarios where t-statistic could be an alternative to z-score:
1. Small sample sizes: When dealing with small samples (typically less than 30), the t-test is preferred because it considers the variability within the sample, taking into account the uncertainty caused by the limited data. The t-test adjusts for the smaller sample size by using the degrees of freedom and provides more accurate results compared to the z-test.
2. Unknown population standard deviation: The t-test is appropriate when the population standard deviation is unknown and needs to be estimated based on the sample data. Typically, the sample standard deviation is used as an estimate, which makes the t-test more suitable in such cases.
3. Non-normal distributions: While the t-test assumes the data to be normally distributed, it is still robust to deviations from normality, especially when the sample size is reasonably large. This makes it a suitable alternative to the z-test in situations where the assumption of normality is not met.
In summary, the t-test can be employed in hypothesis testing for both directional and non-directional hypotheses. It is particularly useful when dealing with small samples, unknown population standard deviation, or non-normal distributions. By using the appropriate t-test based on the research question and data characteristics, researchers can make informed inferences and draw meaningful conclusions.