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A study was conducted in 2018 comparing the average earnings (average annual salaries) of US citizens in each state. Suppose you are hired to provide a more recent comparison of the average salaries of US citizens by state. Specifically you are tasked to determine whether the average salary in California, Washington, and Arizona are identical. Assume that the annual salaries for each state are known to be normally distributed. The data table below shows the annual salaries of the 10 individuals from your survey from each state for this year.   Annual Salaries by State California Arizona Washington $78,080 $64,128 $79,966 $74,610 $64,310 $76,491 $76,127 $61,000 $79,674 $79,951 $61,473 $78,976 $78,808 $58,283 $80,517 $75,243 $62,311 $79,586 $78,191 $61,939 $77,306 $79,793 $58,499 $79,590 $74,424 $61,061 $80,506 $77,776 $64,618 $76,293   Carry out the appropriate hypothesis test at the

Suppose you have a standard deck of 52 playing cards and you randomly select 1 card and record whether or not the card that you drew was a “club”. You then return to the card back to the deck and repeat this process a total of 6 times so that you end up drawing 6 cards total. Find the probability that less than 2 out of the 6 cards that you drew were clubs.  Make sure to type in your answer rounded to 2 decimal places. For example, if you thought the answer was 1.23456, then you would type in 1.23. Note: In a standard deck of playing cards, 13 of them are clubs and 39 of them are not. 

On average, how many hours per week do you spend working at your job(s)?

Daniel was playing a board game with his family and he felt as if the die that they were using was an unfair die because it appeared as if some numbers were occurring more frequently than others, and he didn’t believe this was just due to random chance. Therefore, at the end of the game night, Daniel decided to roll the die 60 times and record the number of times that each number appeared. Those results are shown in the table below.  Dice Counts Number on Die 1 2 3 4 5 6 Count 7 20 6 8 7 12   Use this information to carry out an appropriate test at the

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in Ravenclaw given that they are in year 7.   Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is in year 5 and from Ravenclaw.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Select the term/concept below that most closely matches the following definition: “The occurrence of one event does not effect the probability assigned to the occurrence of the second event”

A professor was interested in comparing how well her students performed on their midterm and final exams in her calculus course. She randomly sampled 7 students from her class and recorded their midterm and final exam grades which are shown in the table below.  Midterm and Final Exam Grade Comparisons Student X=Midterm Exam Y=Final Exam Student 1 75 86 Student 2 73 77 Student 3 87 70 Student 4 90 92 Student 5 72 95 Student 6 84 93 Student 7 91 89   Use this information to calculate Pearson’s correlation coefficient.  Make sure to type your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.  

Consider the table below that shows how many students from each year are in each of the Hogwart’s houses. Use this information to answer the probability question that follows.  Hint: I would recommend finding the totals for each row and column first.  Probability Table Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Ravenclaw 30 38 34 33 39 31 35 Hufflepuff 36 33 29 37 39 35 34 Gryffindor 32 36 41 32 33 35 35 Slytherin 34 32 36 39 33 32 31   Find the probability that a randomly selected student is from Year 6.    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was , then you would type in 0.431.

Ryan is a huge college basketball fan and prior to the start of the NCAA tournament he decides to figure out the odds that his team will win the entire tournament and therefore, the championship. He finds that the odds that his team will win the entire tournament is 1:3. What is the probability that his team wins the championship?   Make sure to write your answer as a decimal rounded to 2 decimal places. For example, if you thought the answer was  then you would type in 0.31.