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State if each of the below statements are true or false statements.  In a confidence interval for the population mean, the margin of error is the same as the standard error. This is a [select1] statement.  t distribution is symmetric around zero. This is a [select2] statement 

In a graduate level Intro to Statistics class, final letter grading scale provided in the syllabus is as follows: Letter Grade Minimum Percentage A 93% A- 90% B+ 87% B 83% B- 80% C+ 77% C 70% D 60% F 0% Usually about about 15% of the students receive at least an A- (i.e.: A- or above) in the course. In this setting, the value “90” is known as:

Please note that this question consists of three parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  Fifty six percent of all Americans have a workplace retirement plan, 68% have health insurance, and 49% have both benefits. If we randomly select a worker:  Are having these two benefits: Retirement and Insurance, mutually exclusive? Explain your answer.   What is the probability that he/she has neither benefits? What is the probability that he/she has health insurance, if he/she has a retirement plan?   

In a graduate level Intro to Statistics class, final letter grading scale provided in the syllabus is as follows: Letter Grade Minimum Percentage A 93% A- 90% B+ 87% B 83% B- 80% C+ 77% C 70% D 60% F 0% Usually about about 15% of the students receive at least an A- (i.e.: A- or above) in the course. In this setting, the value “90” is known as:

In an exit survey, the students were asked, “how likely they are to recommend the program to others”. The response could be: Very unlikely Unlikely Neutral Likely Very likely  After the data collection, the underlying the variable in the dataset would be 

In an exit survey, the students were asked, “how likely they are to recommend the program to others”. The response could be: Very unlikely Unlikely Neutral Likely Very likely  After the data collection, the underlying the variable in the dataset would be 

Please note that this question consists of five parts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.  A college english professor wants to see how reliably the students can distinguish between the “human-written text” and “Gen AI-produced text”. According to some recent research about 70% of the times a randomly chosen student can correctly identify the source.  The instructor shows 15 short passages to his students. Some of these were written by humans whereas the others were GenAI produced (unknown to the students). For each passage, the students were tasked with identifying if it was human or AI written. For a randomly chosen student in the class, let X be the number of incorrect guesses. Assuming guesses are independent: What is the distribution of X? Clearly state the parameters of the distribution.  Write down the probability mass function, for the random variable X defined above. What is the chance that the student correctly identifies the source for all 15 passages (i.e.: zero incorrect guesses)?  What is the chance that the student will make at least one incorrect guess?  What is the probability of making at least one but no more than 6 incorrect guesses.   

Here is a copy of the Z table (Do not click on the downarrow. Click on the file name to open the table within spacer) Z table.pdf  

Suppose we are given the relationship between X and Y where a=`a` and b=`b` We also know that the sample mean for X is  and the sample standard deviation for X is . Find the standard deviation for Y.  

You are allowed one sheet of blank scrap paper for every quiz and exam.