PSY230 Miller M3 Assignment (30 points) Spring A 2024 Things to Review Before Starting the Assignment: 1. Complete the guided Practice Problems first if you have not already done so. It will help you become proficient in answering the questions in this assignment. 2. Check out the module, Assignment Guides, which contains tutorials on how to show the path/process work, essential procedures in Word and Excel, and APA formatting examples. How to Successfully Complete this Assignment: 1. Use this Word document to fill in the answers to the questions. You must type out a clear answer to each question, even if the answer is also contained in the Excel file submitted to show work. 2. Download the Excel file for this assignment and use that data set to answer questions throughout the assignment. 3. All calculation processes must be included to receive full credit. You can use the (1) standard calculation method or (2) alternative excel method (see 'Assignment Guides' module > 'Showing Math Work'). Note: To avoid losing any unnecessary points, be sure to take note of all point deductions and totals found in red underneath each question to ensure you meet the required criteria. Q1. Hypothesis Testing with a Z test (10 points total) A research institute examined the IQs (intelligence quotients) in American adults and reported a mean (u) of 100 points and a standard deviation (o) of 15 points. But I wonder if the statistics in my city, Las Cruces, would be different from the national average. Specifically, I have a hunch that individuals in Las Cruces might have higher IQs compared to the national average. To test this idea, I randomly picked 20 friends of mine living in Las Cruces and asked them their individual IQs. The data set is shown below. (The same data are also provided in an Excel file if you choose to use Excel for your calculations.) I would like to perform a Z test to see if the IQs in Las Cruces (represented by the sample of 20 individuals) are significantly higher than the national average IQ. The significance level for my Z test was set at a = .05. The hypotheses should be directional because I am predicting a specific direction of difference, and the test should be one-tailed. Subject IQ 1 93 2 109 3 94 4 98 5 99 6 128 7 92 8 106 9 114 All course content and materials, including this assignment and all other items published within the Camas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304-06, "Commercial Note Taking Services" and ABCR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement. PSY230 Miller 10 118 11 122 12 94 13 115 14 109 15 87 16 110 17 92 18 108 19 86 20 95 Spring A 2024 Q1a. What is the dependent variable in this study? [1 point] DV=IQ (intelligence quotients) scores Q1b. What should be my null and alternative hypotheses? State each hypothesis using both words and statistical symbol notation. [2 points] 1 for each hypothesis: 0.5 for written, 0.5 for notation Written The mean IQ in Las Cruces is not Greater than the Null national average mean The mean IQ in Las Cruces is Greater than the national Alternative average mean Symbolic Symbol bank for copy & pasting: QNational Q1c. Calculate the sample mean. Round the result to the hundredth (2nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly 93+109+94+98+99+128+92+106+114+118+122+94+115+109+87+110+92+108+86+95=2069 2069/20 Mean=103.45 Q1d. Calculate standard error using the population standard deviation given in the research scenario (SE, which is the standard deviation of the sampling distribution) Round the result to the hundredth (2nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly SE=/sqrt{N} SE=15/sqrt{20} SE=3.35 Q1e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) Round the result to the hundredth (2nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly All course content and materials, including this assignment and all other items published within the Camas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 30-06, "Commercial Note Taking Services" and ABCR Policy 5.308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement. PSY230 Miller Z=(M-)/SE Z=(103.45-100)/3.35 Z=1.03 Spring A 2024 Q1f. Determine the critical Z value(s). Explain how you find the answer. [1 point] 0.5 for the Z value, 0.5 for the rationale Our critical Z value is 1.64 because our a=.05 and because we are conducting a one tailed test due to our hypothesis being greater, we are comparing it to the left side of the distribution. Since it is one tailed, we look up 5% in the tail to give us the critical Z Value. Critical Z Score=1.64 Q1g. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test. - Is the Z statistic more extreme than the critical Z? [0.5 point] - Do you "reject" or "fail to reject" the null hypothesis? [0.5 point] The Z statistic is 1.03 and less extreme than the critical Z value (1.64) So we fail to reject the null hypothesis. Q1h. Write a sentence to answer the research question (you can use the wording from the hypotheses or explain it in another way) [1 point] We fail to reject the null hypothesis because the mean IQ in Las Cruces is not Greater than the national average mean. Q1i. Calculate the standardized effect size Round the result to the hundredth (2nd place to the right of the decimal). [1 point total] deduct 0.5 if the process is correct but the result was calculated incorrectly d= (M-)/ d=(103.45-100)/15 d=0.23 Q2. Hypothesis Testing with a Z Test (7.5 points) According to the CDC report, the mean life expectancy in the US population is currently () 78.2 years with a standard deviation () of 9.6. A researcher examined the age of death of 70 people recently recorded in several Vermont hospitals and calculated the mean to be 81.3 years old. He runs a two- tailed Z test with = .05 to see if Vermont has a significantly different life expectancy compared to the US population. Because the researcher is not predicting a direction, the hypotheses should be non- directional, and the test should be two-tailed. Q2a. What is the dependent variable in this research question? [.5 point] Dependent variable is the life expectancy in individuals. Q2b. What should the null and alternative hypotheses? State each hypothesis using both words and statistical symbol notation. [2 points] 1 for each hypothesis: 0.5 for written, 0.5 for notation All course content and materials, including this assignment and all other items published within the Camas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 30-06, "Commercial Note Taking Services" and ABCR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement. PSY230 Miller Spring A 2024 Written The life expectancy in Vermont is not significantly Null different then the life expectancy nationally. The life expectancy in Vermont is significantly different Alternative then the life expectancy nationally. Symbolic Symbol bank for copy & pasting: PSY230 Miller Spring A 2024 Q3. Hypothesis testing using a Z test (12.5 points) A professor has been teaching introductory statistics for many years and the final exam performance has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e., population) of final exam scores has a mean (u) of 25.4 points (out of a maximum of 30 points) and a standard deviation (o) of 1.62 points. The professor would like to revise the course design to see if student performance on the final exam could be improved. There were 15 students who took the new course as a trial run in a recent academic year, and their average final exam score was 25.9. The professor would like to run a hypothesis test to see if this sample of students in the recent trial course performed significantly better than the past population. In other words, the hypothesis was a comparison between the population taking the course with the new design (represented by the sample of 15 students) with the population taking the course with the old design. The professor is predicting an increase of final exam score with the new design, so the hypotheses should be directional, and the test should be one-tailed. The significance level is set at a = .1. Q3a. Identify the dependent variable for this study [0.5 point] The dependent variable is final exam scores. Q3b. State the null hypothesis and alternative hypothesis using both words and symbol notation. [2 points] 1 for each hypothesis: 0.5 for written, 0.5 for notation Written The new course design students did not perform Null significantly better than the old course design students Symbolic Symbol bank for copy & pasting: Old Alternative better than the old course design students Q3c. Calculate standard error (SE, which is the standard deviation of the sampling distribution) Round the result to the hundredth (2nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly SE=0/sqrt{N} SE=1.62/sqrt {15} SE=0.42 Q3d. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) Round the result to the hundredth (2nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly Z=(M-)/SE Z= (25.9-25.4)/0.42 Z=1.19 All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304-06, "Commercial Note Taking Services" and ABCR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement. PSY230 Miller Spring A 2024 Q3e. Determine the critical value for Z. Explain how you come up with the answer. [1 point: 0.5 for the answer and 0.5 for the rationale] = 0.1, one tail= 10% in tail Critical Z value= 1.28 Q3f. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test. What is the answer to the research question? - Do you "reject" or "fail to reject" the null hypothesis? [0.5 point] - What is the answer to the research question? [0.5 point] The Z statistic of 1.19 is less extreme than the critical Z value of 1.28 the Z statistics fall short of the cut off, so we fail to reject the null hypothesis. Q3g. Calculate the standardized effect size for this test. [0.5 point, must show the process to earn the credit] Is this considered a small, medium, or large effect according to the Cohen's d standards? [0.5 point] d=(M-)/ d= (25.9-25.4)/1.62 d=0.31 It is considered medium because it is more than 0.2 but less then 0.5 Answer the following questions based on this alternative scenario: Because a sample of 15 students is very small, it may not represent a full class adequately. So, the researcher decides to continue to collect data for another semester of the new course design until the sample becomes 80. The average new test score remains 25.9, the same as the previous scenario. All other aspects of the study remain unchanged. Q3h. What is the standard error with this sample? Round the result to the hundredth (2nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly SE=0/sqrt{N} SE=1.62/sqrt {80} SE=0.18 Q3i. What is the Z statistic with this sample? Round the result to the hundredth (2nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly Z=(M-)/SE Z= (25.9-25.4)/0.18 Z=2.78 Q3j. Compare the Z statistic with the appropriate critical Z value and then draw a conclusion about the result of the hypothesis test. What is the answer to the research question now? - Do you "reject" or "fail to reject" the null hypothesis? [0.5 point] - What is the answer to the research question? [0.5 point] The Z statistic of 2.78 is more extreme than the critical Z value of 1.2 so we reject the null hypothesis. This scenario has a larger sample size to work with, so we reject the null hypothesis. All course content and materials, including this assignment and all other items published within the Camas course shell, are copyrighted materials and students may not share outside the dass, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304-06, "Commercial Note Taking Services" and ABOR Policy 5-308 F.14 for more information) Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement. PSY230 Miller Spring A 2024 Q3k. Calculate the standardized effect size. [1 point] 0.5 if the process is correct but the result was calculated incorrectly d=(M-)/ d= (25.9-25.4)/1.62 d=0.31 Q31. Based on the hypothesis test results with the two samples (one with 15 subjects and the other with 80 subjects), how did the increase in sample size impact the test results in terms of the Z statistic and the effect size? [1 point: 0.5 for impact on Z statistic; 0.5 for impact on the effect size] The Z statistic increased by a value of 1.59 but the effect size remained the same. All course content and materials, including this assignment and all other items published within the Canvas course shell, are copyrighted materials and students may not share outside the class, upload to online websites not approved by the instructor, sell, or distribute course content or notes taken during the conduct of the course (see ACD 304-06, "Commercial Note Taking Services" and ABCR Policy 5-308 F.14 for more information). Students must refrain from uploading to any course shell, discussion board, or website used by the course instructor or other course forum, material that is not the student's original work, unless the students first comply with all applicable copyright laws; faculty members reserve the right to delete materials on the grounds of suspected copyright infringement.