Instructions

This week, you have read about hypothesis testing and will now apply this knowledge by writing a paper that addresses the following:

Provide an example of a hypothesis where a one-tailed hypothesis test would be used.

Provide an example of a hypothesis where a two-tailed hypothesis test would be used.

If a researcher has set alpha at 0.05 for a two-tailed hypothesis test, what is the p-value required to reject the null hypothesis?

A researcher has set alpha at 0.05. When the researcher analyzes the data from the experiment using a software program, she obtains a p-value equal to 0.932. Based on this p-value, should the researcher reject the null hypothesis or fail to reject the null hypothesis? Please explain your answer.

A researcher has set alpha at 0.01. When the researcher analyzes the data from the experiment using a software program, he obtains a p-value equal to 0.04. Based on this p-value, should the researcher reject the null hypothesis or fail to reject the null hypothesis? Please explain your answer.

A researcher is interested in whether music played during an exam will improve exam performance. Students in one class listen to music during an exam and students in another class take the exam in silence. The researcher set alpha at 0.05. Test scores for both classes are compared using a statistical software program. The mean test score for the class that listened to music during the exam is 95, while the mean test score for the class that took the exam in silence is 82. The obtained p-value from the independent groups t-test is 0.02. Be sure to answer the following questions:

State the null and alternative hypothesis.

Determine if this is a directional or non-directional test. Please explain your answer.

Establish the conclusion of this study based on the p-value and the means provided.

Describe the Type I error for this study.

Describe the Type II error for this study.

Length:1-2 pages

Your paper should demonstrate thoughtful consideration of the ideas and concepts presented in the course by providing new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards.

https://www.statsdirect.com/help/default.htm#basics/p_values.htm

https://journals.lww.com/inpj/fulltext/2009/18020/hypothesis_testing,_type_i_and_type_ii_errors.13.aspx

https://fod-infobase-com.eu1.proxy.openathens.net/p_ViewVideo.aspx?xtid=111520https://fod-infobase-com.eu1.proxy.openathens.net/p_ViewVideo.aspx?xtid=111520

One of the most important uses of statistics is in analyzing data from research studies. Psychological scientists want to do more than describe samples using the measures of central tendency and variability we discussed during the past 3 weeks. The primary focus of inferential statistics tests is to determine whether group differences are likely due to chance or to real differences between groups.

Prior to data collection, a null and alternative hypothesis are formulated. For example, if we want to determine whether receiving tutoring increases the SAT scores of high school students compared to students who do not receive tutoring, we could randomly assign some students to a group that receives tutoring, and then we could randomly assign other students to a group that does not receive tutoring. Before conducting this study, we would make our prediction (i.e., the alternative hypothesis). The null and alternative hypotheses could be stated as follows:

H0: There is no difference in SAT scores for students who receive tutoring compared to students who do not receive tutoring.

H1: Students receiving tutoring score higher on the SAT compared to students who do not receive tutoring.

This is a directional hypothesis and we will use a one-tailed test to test our hypothesis. This is considered directional because we have a specific prediction (i.e., scores will increase due to tutoring). A non-directional hypothesis would simply predict a difference between the two groups; the nature of the difference (increases or decreases in scores) would not be specified. A non-directional hypothesis requires the use of a two-tailed test.

Typically, in psychological research, we set the alpha level at 0.05. Alpha represents the probability of making a Type I error. A Type I error is when we reject the null hypothesis when it is actually true. In other words, we say we have found a significant difference between groups when in fact the difference is not significant. For example, in the study investigating whether receiving tutoring increases the SAT scores of high school students compared to students who do not receive tutoring, a Type I error is rejecting the null hypothesis and concluding that tutoring does increase SAT scores when it does not.

In addition to Type I errors, we also must be concerned about Type II errors. A Type II error occurs when we incorrectly make the decision to fail to reject the null hypothesis. In other words, we say there is no significant difference between groups when in fact there is a significant difference. For example, a Type II error is falsely concluding that tutoring has no effect on SAT scores.

Alpha is set by the researcher before conducting the analysis. When using statistical software to conduct hypothesis tests, we are provided with a p-value for the test. As mentioned in the assigned reading, a p-value is a probability and can range in value from 0-1.0. If the p-value is less than alpha, we can reject the null hypothesis. The p-value represents the probability that the result occurred by chance and is not due to true group differences.

Remember, if we have a two-tailed test and have set alpha at 0.05, then we need a p-value less than 0.025 in order to reject the null hypothesis. This is because we are looking at both sides of the distribution in a two-tailed test. In order to keep alpha at 0.05, we must divide this over both ends of the distribution (0.025 + 0.025 = 0.05). For a one-tailed test, we are only looking at one side of the distribution, so we can reject the null hypothesis when p-values are less than 0.05.

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