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WORK MUST BE SHOWN ON THIS QUESTION TO RECEIVE CREDIT. Test the claim that the samples come from populations with the same mean.  Assume that the populations are normally distributed with the same variance. A consumer magazine wants to compare the lifetimes of ballpoint pens of three different types.  The magazine takes a random sample of pens of each type in the following table. Brand 1 Brand 2 Brand 3 260 181 238 218 240 257 184 162 241 219 218 213 Do the data indicate there is a difference in the mean lifetime for the three brands of ballpoint pens?  Use

Solve the problem. In a certain lottery, five different numbers between 1 and 40 inclusive are drawn.  These are the winning numbers.  To win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn.  What is the probability of winning? (Give your answer as a fraction.)  

WORK MUST BE SHOWN ON THIS QUESTION TO RECEIVE CREDIT. Use the empirical rule to solve the problem. The amount of Rachel’s monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8.  What percentage of her phone bills are between $31 and $79. [a1]%

WORK MUST BE SHOWN ON THIS QUESTION TO RECEIVE CREDIT. Use the given information to find the P-value.  Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z=0.52. The p-value is [a1]. (Round to three decimal places as needed.) State the correct conclusion about the null hypothesis. [a2]

Determine whether the given procedure results in a binomial distribution.  If not, state the reason why.   Tossing a fair coin 10 times and noting the number of times that the coin lands heads up.

WORK MUST BE SHOWN ON THIS QUESTION TO RECEIVE CREDIT. Solve the problem. How many ways can the IRS auditor select 3 of 10 tax returns for an audit?

A relation R has attributes A, B, C, D, E, F, G, H, I, J, and satisfies the following FDs: ABD -> EAB  -> GB   -> FC   -> JCJ  -> IG   -> H Please find the candidate key. Please provide the key; no need to show any steps. [Hint: it is a four-letter key like ABJC or EHGF, so do not waste your time computing closure of A, B, then AB, AC, and then ABC BCA, etc. Go directly to four-letter’s closures]

1. Pick your favorite piece of art that we have studied this semester. Your chosen piece cannot be one that has been discussed in the exam so far, nor one that you have already used as an answer. Include the artist, title, and date, and the lecture title where each piece was discussed. 2. Which time period, art movement, or culture is your chosen piece associated with? 3. Define the artistic style that is typically associated with that time period, art movement, or culture. What type of art do we normally see in this era or culture? 4. Does your chosen piece align with the type of art seen in this era or culture, or does it stick out as different? Why? 5. Explain why you like this piece or feel a connection to the work. 100 words minimum

Only for question 4, you are allowed to use paper submission. Please draw the diagram(s) on paper and email them to me within 10 minutes of your submission of the final exam on Canvas. Please remember that any paper emailed to me more than 10 minutes after the final exam submission on Canvas will not be considered for grading.  Additionally, please ensure your handwriting is legible. Alongside the answer to question 4, please email me any scratch paper(s) that you have used during the exam.   For all the questions, try to explain the intermediate steps. Providing the answer will only earn you 1 point for the question. Also, even if you do not get the final answer right, showing me the steps will help you to get partial credits, which is more than 1 point. Also, please take your time in answering the questions. Please do not rush and read them carefully.  

Marjorie, a retired teacher, was close to her grandchildren, Eli and Jackson, whom she helped raise after their parents passed away. In 2018, Marjorie drafted a will leaving “all my personal property to Eli and my real property to Jackson.” Marjorie also named her close friend, Simon, as executor. The will did not include a residuary clause. Marjorie signed the will in front of Simon and another friend, Fred, but did not date it. Simon and Fred both signed the will as witnesses. In 2021, after a serious argument with Jackson about selling the family cabin, Marjorie handwrote a short note that said: “I want Eli to have the cabin now because Jackson doesn’t appreciate the family history of the cabin.” Marjorie signed and dated the note and placed it into her recipe book. Marjorie told Eli to “keep this safe.” The note did not mention any other property. A week before Marjorie died in 2024, Marjorie had secretly sold the cabin and used the money to buy stocks in ABC Company. It was stipulated that Marjorie had full mental capacity during her lifetime. What are the respective interests of Eli and Jackson in Marjorie’s estate? Answer according to California law only.