Five Steps of Hypothesis Testing
6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
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a. Use the five steps of hypothesis testing.
b. Figure the confidence limits for the 95% confidence interval.
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References
Five Step Hypothesis Testing Procedure
The examples on the following pages use the five step hypothesis testing procedure outlined below. This is the same procedure that we used to conduct a hypothesis test for a single mean, single proportion, difference in two means, and difference in two proportions.
Step 1: Check assumptions and write hypotheses
When conducting a chi-square goodness-of-fit test, it makes the most sense to write the hypotheses first. The hypotheses will depend on the research question. The null hypothesis will always contain the equalities and the alternative hypothesis will be that at least one population proportion is not as specified in the null.
In order to use the chi-square distribution to approximate the sampling distribution, all expected counts must be at least five.
To check this assumption, compute all expected counts and confirm that each is at least five.
Step 2: Compute the test statistic
In Step 1 you already computed the expected counts. Use this formula to compute the chi-square test statistic:
Step 3: Determine the p-value
Construct a chi-square distribution with degrees of freedom equal to the number of groups minus one. The p-value is the area under that distribution to the right of the test statistic that was computed in Step 2. You can find this area by constructing a probability distribution plot in Minitab Express.
Step 4: Make a decision
Unless otherwise stated, use the standard 0.05 alpha level.
reject the null hypothesis.
fail to reject the null hypothesis.
Step 5: State a real-world conclusion
Go back to the original research question and address it directly. If you rejected the null hypothesis, then there is evidence that at least one of the population proportions is not as stated in the null hypothesis. If you failed to reject the null hypothesis, then there is not evidence that any of the population proportions are different from what is stated in the null hypothesis.
ADDITIONAL INSTRUCTIONS FOR THE CLASS
Discussion Questions (DQ)
- Initial responses to the DQ should address all components of the questions asked, include a minimum of one scholarly source, and be at least 250 words.
- Successful responses are substantive (i.e., add something new to the discussion, engage others in the discussion, well-developed idea) and include at least one scholarly source.
- One or two sentence responses, simple statements of agreement or “good post,” and responses that are off-topic will not count as substantive. Substantive responses should be at least 150 words.
- I encourage you to incorporate the readings from the week (as applicable) into your responses.
Weekly Participation
- Your initial responses to the mandatory DQ do not count toward participation and are graded separately.
- In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies.
- Participation posts do not require a scholarly source/citation (unless you cite someone else’s work).
- Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.
APA Format and Writing Quality
- Familiarize yourself with APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required).
- Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation.
- I highly recommend using the APA Publication Manual, 6th edition.
Use of Direct Quotes
- I discourage overutilization of direct quotes in DQs and assignments at the Masters’ level and deduct points accordingly.
- As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content.
- It is best to paraphrase content and cite your source.
LopesWrite Policy
- For assignments that need to be submitted to LopesWrite, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me.
- Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes.
- Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own?
- Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for tips on improving your paper and SI score.
Late Policy
- The university’s policy on late assignments is 10% penalty PER DAY LATE. This also applies to late DQ replies.
- Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances.
- If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect.
- I do not accept assignments that are two or more weeks late unless we have worked out an extension.
- As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.
Communication
- Communication is so very important. There are multiple ways to communicate with me:
- Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class.
- Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.
