M2 Assignment

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Arizona State University *

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45826

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Statistics

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Apr 3, 2024

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PSY230_Bienemann Spring 2024 M2 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 in Q1. 3. All calculation processes must be included to receive full credit, this includes for calculating simple probabilities . 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. Simple Probability (3 points) Download the Excel data file for Q1 to answer this set of questions. For each question, compute the probability of randomly selecting a case from the data set with the target variable attribute. Be sure to show the calculation process. The Excel file only needs to be submitted if you are using the file to show your work/process. Round to the thousandth (3rd decimal place to the right if/when necessary, otherwise do not round the probabilities). Calculation process must be included in this document or in a supporting Excel file to earn the credit Helpful tips: ● Being able to sort the data will be helpful for answering these questions. Review the Excel tutorials in the “Assignment Guides”. ● These questions are simple probability questions based solely on the data set provided in the Excel file. They have nothing to do with calculating z or finding proportions in the z table. ● Probability is always expressed in the decimal format (e.g. .15, .4, .975… etc), not as a fraction or percentage (these formats will not be accepted as correct answers). Round to the thousandth (3 rd decimal place to the right if/when necessary, otherwise do not round the probabilities). Q1a. What is the probability of drawing a male? [0.5 point] 24/40= 0.6 Q1b. What is the probability of drawing a person who is older than 76 years old? [0.5 point] 26/40= 0.65 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 Q1c. What is the probability of drawing a person who has an IQ score lower than 110 (excluding 110)? [0.5 point] 29/40= 0.725 Q1d. Identify the marital status group that has the highest probability of being drawn from the group of subjects, then calculate that probability. [0.5 point] The marital status that has the highest probability of being drawn is married. The probability of married is 13/40= 0.325 Q1e. What is the probability of drawing a divorced person in their 90s? [0.5 point] There are two 92-year-olds and neither one of them is divorced. 0/40= 0 Q1f. What is the probability of drawing a female (out of the total subject count, not just females) with an IQ greater than 110? [0.5 point] 3/40= 0.075 Q2. Comparing different distributions using Z scores (3 points) Note: It is not necessary to use the Excel data set for this set of questions, however, the data is included on the sheet labeled “Q2” for convenience. Gavin and Grace have both taken PSY230 last year and they are curious about who did better in that course. The problem is, they were in two different sections with two different point systems. To figure out how each of them did within their own classes, they decide to calculate their own Z scores in order to directly compare how well they did relative to their respective classmates. If the calculation process (or rationale) is correct but the answer is wrong, deduct 0.5. *Find a blueprint for your work on sheet Q2 in the M2_Data Excel file Q2a. Grace earned 408.5 points in her stats course. Her professor’s overall class average was 371 points with a standard deviation of 30 points. What was Grace’s Z score? [1 point] Z = (X - µ)/ó = (408.5 - 371)/30=1.25 Grace's Z score is 1.25 Q2b. Gavin earned 87 points in his stats course. His professor’s overall class average was 75 points with a standard deviation of 6 points. What was Gavin’s Z score? [1 point] 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 Z = (X - µ)/ó = (87 - 75)/6=2 Gavins Z score is 2 Q2c. Who did better in the stats course in terms of class standing in each section? How did you know? [1 point] Gavin did better in the stats course in terms of class standing and I know this because Gavin’s Z score is higher meaning even though Grace’s score is higher Gavin’s score is higher relative to the class standing. Q3. Proportions (percentages) in a Z Distribution (10 points) Note: It is not necessary to use the Excel data set for this set of questions, however, the data is included on the sheet labeled “Q3” for convenience. A standardized visual working memory test has a population mean (μ) of 152 and a standard deviation (σ) of 16. Because the scores are normally distributed, the whole distribution of scores can be converted into a Z distribution. Each raw score in the original distribution has a corresponding Z score in the Z distribution. The Z distribution has a symmetrical bell shape with known properties, so it’s possible to mathematically figure out the percentage of scores within any specified area in the distribution. Deduct 0.5 if the calculation process is correct but the result is wrong Helpful tips: To answer the following questions, it helps to draw a Z distribution (bell curve) and place an individual’s Z score on the distribution as a visual aid. Use the Z table for converting between Z score and area (percentage) of the distribution marked by this Z score. Use this Normal Distribution Table to visualize how your z scores are plotted on a normal distribution: https://www.mathsisfun.com/data/standard-normal-distribution-table.html *Find a blueprint for your work on sheet Q3 in the M2_Data Excel file Q3a. Jenny has a score of 143. What is Jenny’s Z score? Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] Z = (X - µ)/ó = (143-152)/16 = 0.56 Q3b. What is the percentage of students that score lower than Jenny? [1 point] P(Z<-0.56) = .2123 = 21.23 % = 21.23% 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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PSY230_Bienemann Spring 2024 P(Z<-0.56) = .2123 = 21.23 % = 21.23% P(Z<-0.56) = .2123 = 21.23 % = 21.23% P(Z<-0.56) = .2123 = 21.23 % = 21.23% P(Z<-0.56) = .2123 = 21.23 % = 21.23% P(Z<-0.56) = .2123 = 21.23 % = 21.23% Q3c. Based on the Z table, if 500 students take the test, how many of them would likely score above Jenny’s score? (Round the answer to a whole number) [1 point] Number of students above Jenny’s score = 1 - .2123 = .7877 1 Q3d. Nicole has a score of 170. What is Nicole’s Z score? Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] Z = (X - µ)/ó = (170 – 152)/16 = 1.13 Z= 1.13 Q3e. What is the percentage of students that score lower than Nicole? [1 point] P(Z<1.13) = .1292 % = 12.92% 12.92% score lower than Nicole Q3f. Based on the Z table, if 250 students take the test, how many of them would likely score below Nicole’s score? (Round the answer to a whole number) [1 point] 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 32 Students out of 250 would likely score below Nicole. 250(.1292)= 32 Q3g. What is the percentage of students that score between Jenny and Nicole? [1 point] P(-.56<Z<1.13) = .1292 - .2123 = .0831 % = 8.31% Q3h. Molly scores at the 91 st percentile on this exam, what is her Z score? [1 point] Hint: A score at 91 st percentile means 91% of the scores are below this score. Z= 1.34 Q3i. Based on the result of the previous question, what is Molly’s raw score of working memory? Round the result to the hundredth (2 nd place to the right of the decimal). [1 point] (X – 152)/16 = 1.34 pemdas 16*1.34+152= 173.44 Q3j. What would be the median raw score on this exam? [1 point] Hint: Review the definition of “median” and then figure out the percentage of scores below (or above) this score. The median and the mean are the same and the mean is 152 so the median is also 152 Q4. Z Distribution: From Probabilities to Proportions (percentages) (7 points) Answer the following questions with this scenario: A school district runs a gifted language program in fourth grade with a selection criterion of 97 th percentile. That is, students who score at 97 th percentile or above on a standardized language test are eligible for the gifted program. Answer the following question based on this scenario. Helpful tips: Review the tutorial videos on “how to use the Z table” before answering the following questions. 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 Q4a. What is the probability of randomly drawing a student from the whole population of fourth- graders that would meet the selection criterion for the gifted program? Explain how you determined the answer. [1 point] Both the answer and the rationale must be correct to earn the credit 1 -.97 = .03 I determined this as my answer, because if you were trying to find the probability of randomly drawing a student from the whole population in 4 th graders, you would have to take it out from the full 100% out of the 97 th percentile. So I did 100% - 97% except in decimal form to find out that it would come to 3%. Q4b. If the district has 400 fourth-graders in total, how many will be eligible for the gifted program? (Round the answer to a whole number) [1 point] Deduct 0.5 if the process is correct but the result was calculated incorrectly 400(.03)= 12 12 students Q4c. If we use a Z distribution to represent all the test scores from the fourth-graders, what is the Z score that serves as the critical (or cutoff) value for determining eligibility for the gifted program? [2 points] Both the answer and the rationale must be correct to earn the credit. Because the Z score that is shown for the 97 th percentile is 1.88. The Z distribution to represent the test scores for the students that would determine eligibility as 1.88 Q4d. This standardized test used for the screening process has a published raw score mean (μ) of 254 and standard deviation (σ) of 8. Based on the critical Z score (from question c above, what would be the critical test score if we use the original raw scores to determine the students’ eligibility? 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 (x-254)/8 = 1.88 With algebra: 1.88(8)+254=269.04 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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PSY230_Bienemann Spring 2024 X = 269.04, since X is the critical score Z = (X - µ)/ó (x-254)/8 = 1.88 simple math 1.88(8)+254=269.04 X = 269.04 X is the critical score Q4e. Shay has a raw score of 280, is she eligible for the gifted program? Explain your rationale for this answer. [1 point] Both the answer and the rationale must be correct to earn the credit Since Shay has a raw score of 280 she would be eligible for the gifted program because her score is higher than the calculated value is to be eligible. Q4f. Eric has a Z score of 1.79, is he eligible for the gifted program? Explain your rationale for this answer. [1 point] Both the answer and the rationale must be correct to earn the credit (x-254)/8 = 1.92 =269.36 (x-254)/8 = 1.79 x=268.32 Because Eric has a Z score of 1.79. That means he scored a raw score of 268.32 which is lower than the valuated score to be able to be eligible to get into the program. The critical score is 269.04. So he is lower than that and not eligible Q5. Z Distribution: From Probabilities to Proportions (7 points) Answer the following questions with this scenario: In a health initiative, the local school district would like to promote awareness of the students’ BMI (body mass index) and encourage parents of students with extremely high or extremely low BMI to work with the school nurse in improving their children’s health. The school district decides to measure all third-graders’ BMIs, identify the highest 1% and the lowest 1% of the students, and then follow up with their parents. The graph below demonstrates the areas in the BMI distribution for the health program. Helpful tips: Review the tutorial videos on “how to use the Z table” before answering the following questions. 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 Q5a. If we randomly draw one third-grader out of the school district, what is the probability of that child having a BMI that meets the criterion for the health program? Explain how you figure out the answer. [1 point] Both the answer and the rationale must be correct to earn the credit P()=.98 I got .98 because we don’t know the exact. Measurements for every student. But the graph does show a low 1% and a high 1%. Because I took 100 as a whole and I took away the low 1% and the high 1% to the term the other students which came out to .98 Q5b. If the BMI distribution is converted into a Z distribution, what would be the upper critical Z value and the lower critical Z value that mark the two “significant” areas at the tails? [2 points] 1 point for each critical Z ) Explain how you find the answers. [1 point] So the upper critical Z value = 2.33 Lower Critical Z value = -2.33 Q5c. If Abby’s BMI is converted into a Z score of -2.38, is Abby included in the health follow-up program? Explain how you find the answer. [1 point] Both the answer and the rationale must be correct to earn the credit Abby would not be included in the health follow-up program because Abby has a Z score that is higher than the value of 2.33. Q5d. If the school district has a total of 310 third-graders, how many students’ parents will be contacted by the school nurse? (Round the answer to a whole number) [1 point] .5 if the process is correct but the result was calculated incorrectly 310(.02)=6.2=6 6 student parents would be contacted. Q5e. If the school district chooses a different strategy and sets the higher and lower cut-off points at Z values of ±2.4, will the school nurse have more students or fewer students to follow up with, compared 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 to the original cut-offs (1% at the upper and lower ends of the distribution)? Explain how you determined the answer. [1 point] Both the answer and the rationale must be correct to earn the credit The school nurses would have fewer students to follow up with compared to the original cutoffs at 2.33 because the cutoff is now 2.4. meaning that students with a BMI that meets that number for the health program will be increased. This means fewer students will follow up with school nurses. 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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