Blog

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, Arizona, and Texas 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 Texas Arizona $78,080 $65,025 $64,128 $74,610 $66,403 $64,310 $76,127 $65,038 $61,000 $79,951 $63,061 $61,473 $78,808 $66,552 $58,283 $75,243 $66,082 $62,311 $78,191 $69,226 $61,939 $79,793 $64,254 $58,499 $74,424 $65,043 $61,061 $77,776 $66,206 $64,618   Carry out the appropriate hypothesis test at the

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 9 10 10 13 11   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 Hufflepuff and Slytherin.    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.

A researcher was interested in determining whether or not “Money can buy happiness”. He randomly sampled 300 individuals and asked them how much money they make annually as well as how happy they were at this point in their life on a scale from 1-10. He then proceeded to analyze the data and came up with the following regression equation where X represents the amount of money in tens of thousands of dollars that they made (i.e. $75,000 would correspond to 7.5) and Y represents their predicted happiness level:   Use this linear regression equation to predict the an individuals happiness level if their annual income is $80,000.  Type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 6.54321 then you would type in 6.543. 

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 in year 2 and 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.

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 6 5 14 13 11 11   Use this information to carry out an appropriate test at the

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 3:17. 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. 

A potato chip manufacturer was building a new manufacturing plant, and they were trying to decide whether or not they wanted to change the equipment/machine they were currently using to bag the potato chips. They had noticed a wide variability in the weight of the potato chip bags that were being produced with their current equipment, and they wanted to reduce the variability. Therefore, they decided to determine if a newer machine would help them reduce the variability in the weights of the bags. They randomly sampled the weights of 50 bags from their current machine and 50 bags from the new machine and both of them recorded an average weight of 10 ounces. However, the current machine had a standard deviation of 0.16 ounces and the new machine had a standard deviation of 0.09 ounces. Carry out the appropriate hypothesis test at the

In 2019, a survey was conducted to try and determine whether or not MLS games drew in more fans than NBA games. The researchers randomly selected 40 games/matches from each sport and recorded the number of fans in attendance. In the 40 MLS games, there was an average of 21,310 fans per game with a sample standard deviation of 1,211 fans. In the 40 NBA games, there was an average of 17,857 fans with a sample standard deviation of 1,387 fans. Carry out the appropriate hypothesis test at the

Suppose you have a jar that contains 20 marbles: 5 red, 7 blue, 4 green, and 4 black. If you were to select 1 marble at random from the jar, what is the probability that you would pull 1 black marble?   Type in your answer as a decimal rounded to 2 places. For example, if you thought the answer was 54.321% then you would type in 0.54.