Posted: December 18th, 2023

The national average for students on

Hypothesis Testing and Single Sample z test Practice ProblemsNote: unless indicated otherwise, use level of significance of .05 for all questions1. A study was conducted to investigate whether the underperformance of students in highschools in the United States can be reduced. There has been recent interest in the issue of“mindsets” to improve academic performance. It has been shown that individuals with a“growth mindset” (i.e., a belief that students can grow their intelligence and that academicchallenges are an opportunity for growth, rather than a sign that the student is not capable oflearning) may do better in school than those with a “fixed mindset” (i.e., a belief that studentsare born with a fixed level of ability that cannot be changed). To examine this issue, aresearch study was conducted in which a group of 49 high school students were given a 45minute “growth mindset intervention” in which they were taught that the brain can grow andreorganize as a result of hard work and academic challenges. At the end of the school year,the GPA of a sample of students who were given the “growth mindset intervention” wascompared to the overall GPA of all students at the high school. It is known that the overallGPA of students at the high school is 2.40 with a SD of .25. Complete the following steps toconduct a statistical test that addresses if the “growth mindset intervention” leads to adifference in the GPA in high school students.a. What is the Independent Variable (IV) with its respective levels and what is theDependent Variable (DV) in this experiment?b. Step 1: Write the null and research (alternative) hypotheses in symbols.c. Step 2: Assume that we draw all possible random samples of 49 students from thepopulation of students at the high school. What would be the appropriate (i.e., compute)standard error (SE) for a distribution of samples of size 49? Give an interpretation inwords of what this number means.d. Step 2 (continued): The critical value for the test statistic.e. Step 3: Find the obtained (i.e., computed) test statistic for a sample (n=49) with a meanof 2.50.Step 4: Make a statistical decision about the null. Will you reject or fail to reject the null basedon your sample data? (Be sure to include appropriate test statistic and decision criteria).f. Step 4 (continued): Provide a substantive conclusion about the results from your sampledata. (Be sure to include the research context and descriptive statistics).g.Continuing with this example, (i.e. the same population mean, standard deviation, etc.),calculate the effect size of the test anxiety on GPS (using Cohen’s d) for the sample ofstudents in the “growth mindset intervention group” who had a mean GPA of 2.50. Howlarge of an effect size is this, small, medium, or large?h. The following table lists the possible decisions that can be made based on the researchstudy above. Label which boxes would be correct decisions and which would be errors(Type I and Type II).TruthH0 TrueH0 False“Growth MindsetIntervention” does notaffect GPA“Growth MindsetIntervention” doesaffect GPAReject H0“GrowthMindsetIntervention” does affectGPAStatisticalDecisioni.j.Fail to rejectH0“GrowthMindsetIntervention” does notaffect GPAWhat would a Type I error mean in the context of this study?What would a Type II error mean in the context of this study?2. The national average for students on the Science Attitudes Questionnaire is 10.0, witha standard deviation of 1.0. Creative Teaching Elementary School has created a newtextbook which they use in their school because they believe it will increase studentinterest in science. A random sample of 25 students from Creative TeachingElementary School are given the Science Attitudes Questionnaire and their meanscore was 10.2. Go through all 4 steps of hypothesis testing to decide if the newtextbook at Creative Teaching Elementary School significantly impacts students’attitudes about math.a. Step 1: Write out the hypothesesb. Step 2: Assume that we draw all possible random samples of 25 students from thepopulation of students at the college. What would be the appropriate standard error (SE)for a distribution of samples of size 25?c. Step 2 (continued): What is the critical value for this test statistic?d. Step 3: Calculate the test statistice. Step 4: Make a statistical decision about the null. Will you reject or fail to reject the nullbased on your sample data? (Be sure to include appropriate test statistic and decisioncriteria).f. Step 4 (continued): Provide a substantive conclusion about the results from your sampledata. (Be sure to include the research context and descriptive statistics).g. The following table lists the possible decisions that can be made based on the researchstudy above. Label which boxes would be correct decisions and which would be errors(Type I and Type II).TruthH0 TrueH0 FalseNew Textbook atCreative TeachingElementary Schooldoes not affect studentattitudes about scienceNew Textbook atCreative TeachingElementary Schooldoes affect studentattitudes about scienceReject H0New Textbook atCreative TeachingElementary Schooldoes affect studentattitudes about scienceStatisticalDecisionFail to reject H0New Textbook atCreative TeachingElementary Schooldoes not affectstudent attitudes aboutscienceh. What would a Type I error mean in the context of this study?i. What would a Type II error mean in the context of this study?

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