PSY230_M3 Assignment_Spring24 a

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Arizona State University *

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Statistics

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Apr 3, 2024

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PSY230_Bienemann Spring 2024 M3 Assignment (30 points) 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) of Americans and reported a mean ( μ ) of 115 points and a standard deviation ( σ ) of 15 points. But I wonder if the statistics in my city, Chicago, would be different from the national average. Specifically, I have a hunch that individuals in Chicago might have higher IQs compared to the national average. To test this idea, I randomly picked 15 friends of mine living in Chicago and asked them their individual IQs. The data set can be found on sheet Q1 in the M3_Data Excel file. I would like to perform a Z test to see if the IQs in Chicago (represented by the sample of 15 individuals) are significantly higher than the national average IQ. The significance level for my Z test was set at α = .05. The hypotheses should be directional because I am predicting a specific direction of difference, and the test should be one-tailed. Q1a. What is the dependent variable in this study? [1 point] The dependent variable in this study is the IQ’s. 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 Symbolic Symbol bank for copy & pasting:  =      Null The average IQ of people in Chicago is not going to be higher than the H 0 :  IQ American  IQ Chicago 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 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_Bienemann Spring 2024 national average. Alternative The Average IQ of people In Chicago Is higher than the national average. H 1 :  IQ American  IQ Chicago Q1c. Calculate the sample mean. Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] 0.5 if the process is correct but the result was calculated incorrectly 𝑀 = ∑ 𝑋 N 133+92+100+114+122+134+94+112+109+148+129+92+154+120+144 15 M= 119.8 Q1d. Calculate standard error using the population standard deviation σ given in the research scenario ( SE , which is the standard deviation of the sampling distribution) Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly σ m = σ √ N = 15 √ 15 =3.87 Q1e. Calculate the Z statistic (which indicates where our sample mean is located on the sampling distribution) Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] deduct 0.5 if the process is correct but the result was calculated incorrectly Z = M − ❑ m 2 a ❑ Z = 119.8 − 115 3.87 ❑ = 1.24 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 We have a one-tail test And the critical Z value that is on the right side, since we are hypothesizing that the individual IQ in Chicago is higher than the national, α = .05 So that means that I will be on the lookout for 5% in the tail area. So that means that I will be using 5.05% since alpha equals .05. we’re looking for 5%. P( Z > Z crt) =0.05 where Z is the standard normal variable but P( Z > 1.64) = 0.05 the corresponding Z value is 1.64. So the critical Z value is 1.64 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 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_Bienemann Spring 2024 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 less extreme and lower than the critical Z 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] The average IQ of the 15 individuals from Chicago is not higher than the national average IQ of Americans Q1i. Calculate the standardized effect size Round the result to the hundredth (2 nd place to the right of the decimal). [1 point total] deduct 0.5 if the process is correct but the result was calculated incorrectly m-µ/ σ= 119.8-115/15=0.32 Q2. Hypothesis Testing with a Z Test (12.5 points) According to the CDC report, the mean life expectancy in the US population is currently (µ) 85.8 years with a standard deviation ( σ ) of 15.9. A researcher examined the age of death of 80 people recently recorded in several Florida hospitals and calculated the mean to be 89.4 years old. He runs a two-tailed Z test with α = .05 to see if Florida 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. *Find a blueprint for your work on sheet Q2 in the M3_Data Excel file Q2a. What is the dependent variable in this research question? [.5 point] The dependent variable is the life expectancy 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 Written Symbolic Symbol bank for copy & pasting:  =      Null The life expectancy mean in Florida will not be different from the expectancy of H 0 :  =85.8 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 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.

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