PSYC2F23 ChatGPT Assignment #12

PSYC2F23 (Fall/Winter, 23/24) – ChatGPT Assignment 12 (Due ONLINE by Friday, January 26 th )  For each of the following questions, please provide your answers first. When answering each question, please base your responses on the knowledge and concepts we've covered in class.  After you've completed your answers, use ChatGPT as a secondary source to cross-check them.  In instances where ChatGPT might provide incorrect information, don't be concerned. I'll be sharing answer keys, and provide you with ChatGPT's responses that I've reviewed, modified and found helpful for your understanding.  It's ESSENTIAL that you thoroughly read and reflect on this feedback to further your comprehension. 1. Imagine you have to explain to a 10-year-old what a 'sampling distribution of the mean' is, using a fun and easy-to-understand example. After you've come up with your example and explanation, consult with ChatGPT to see if there are any additional creative ideas or ways to simplify the concept further. Your explanation: ChatGPT response: 2. Below is a list of statistical symbols and a list of their definitions. Match each symbol with its correct definition: u x : μ: x : x: s: σ: σ x : IMPORTANT: W HEN UTILIZING C HAT GPT, IT IS VITAL NOT TO MERELY TRANSCRIBE THE ANSWERS . T HE TRUE VALUE OF THIS LEARNING TOOL LIES IN UNDERSTANDING THE EXPLANATIONS PROVIDED . I NVEST TIME IN THOROUGHLY READING AND COMPREHENDING THE REASONING BEHIND EACH ANSWER . T HIS APPROACH WILL NOT ONLY ENHANCE YOUR LEARNING BUT ALSO ENABLE YOU TO APPLY THE KNOWLEDGE MORE EFFECTIVELY IN DIFFERENT CONTEXTS . A CADEMIC HONESTY IS PARAMOUNT . P LAGIARISM , INCLUDING COPYING FROM PEERS , WILL NOT BE TOLERATED . A NY STUDENT FOUND PLAGIARIZING , AS WELL AS THE STUDENT WHOSE WORK WAS COPIED , WILL FACE PENALTIES . T HIS MAY INCLUDE FAILING . Sample standard deviation A raw score Population standard deviation Mean of the sampling distribution of the mean (i.e., the mean of the means) Sample mean Population mean Standard deviation of the sampling distribution of the mean (a.k.a standard error of the mean)

3. We learned in lecture that for a single-sample z test, the critical regions (the areas in the distribution containing all the values that allow us to reject H 0 ) and the critical values (the values that bound the critical regions) are determined by the alpha level (i.e., α = 0.05 or α = 0.01) and the number of tails (i.e., 1-tailed or 2-tailed). Given the different combinations of alpha levels and the number of tails, formulate the decision rule (Step 3 in hypothesis testing) for each scenario. Provide your own answers first and then check with ChatGPT.  If α = 0.05, 2-tailed Decision rule: __________________________________  If α = 0.05, 1-tailed (testing for an increase, i.e., in the positive direction) Decision rule: __________________________________  If α = 0.05, 1-tailed (testing for a decrease, i.e., in the negative direction) Decision rule: __________________________________  If α = 0.01, 2-tailed Decision rule: __________________________________  If α = 0.01, 1-tailed (testing for an increase, i.e., in the positive direction) Decision rule: __________________________________  If α = 0.01, 1-tailed (testing for a decrease, i.e., in the negative direction) Decision rule: __________________________________ 4. For each of the following scenarios, calculate the obtained z-score (Z obt ) and compare it with the critical z-score (Z crit ). Based on your calculation, will you reject or retain the null hypothesis? Provide a rationale for your decision using Z obt and Z crit , and then verify your answer with ChatGPT. a) Population mean ( μ ) = 50, population standard deviation ( σ ) = 10, sample mean ( x ) = 55, sample size ( N ) = 30, alpha ( α ) = 0.05, and 2-tailed test. Your answers: ChatGPT response: b) Population mean ( μ ) = 75, population standard deviation ( σ ) = 12, sample mean ( x ) = 72, sample size ( N ) = 50, alpha ( α ) = 0.01, and 1-tailed test (testing for a decrease). Your answers: ChatGPT response: c) Population mean ( μ ) = 100, population standard deviation ( σ ) = 15, sample mean ( x ) = 108, sample size ( N ) = 25, alpha ( α ) = 0.01, and 1-tailed test (testing for an increase). Your answers: ChatGPT response: d) Population mean ( μ ) = 200, population standard deviation ( σ ) = 30, sample mean ( x ) = 205, sample size ( N ) = 40, alpha ( α ) = 0.05, and 2-tailed test. Your answers: ChatGPT response: