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In which of the following situations would a related-groups t-test be appropriate?

Which of the following null hypothesis statistical tests asks you to compute (M1 – M2) in the numerator?

The fiscal 2023 financial statements for Day-Brite, Inc., report net sales of $62,217 million, net operating profit after tax of $2,478 million, net operating assets of $22,556 million. The 2022 balance sheet reports net operating assets of $21,465 million.         Day-Brite’s 2023 net operating asset turnover is:

The 2023 Form 10-K of Oracle Corporation, for the May 31, 2023 year-end, included the following information relating to their allowance for doubtful accounts: Balance in allowance at the beginning of the year $476 million, accounts written off during the year of $167 million, balance in allowance at the end of the year $379 million.         What did Oracle Corporation report as bad debt expense for the year?

 Capri Inc. reported retained earnings of $185,500 on December 31, 2022. During the year, Capri recorded a net loss of $85,050 and paid dividends of $47,500. The company had no other transactions that affected retained earnings.   What must retained earnings have been on December 31, 2021?

Consider the situation where we want to transmit a sequence of symbols from the alphabet {A,B,C,D}, with frequencies given byA: 0.16, B: 0.34, C: 0.33, D: 0.17In an optimal encoding (as produced by Huffman’s algorithm), how many bits will be used to represent

Finally, some questions about a probabilistic problem. Given a sequence of coin flips, we define a doubleton as two consecutive Hs with no H immediately before or after, or two consecutive Ts with no T immediately before or after. For example, the sequence TTHTTTHHHHTTHTHHThas 3 doubletons (boldfaced). Assume that we toss a fair coin n times (n  >= 3). With X a random variable denoting the number of doubletons in the resulting sequence, we want to calculate E[X].  For that purpose, for each i in 1..n we define an indicator random variable X_i for the event that toss i starts a doubleton; thus E[X_n] = 0 andX = \sum_{i=1}^n X_i.(Observe that when n = 3 we have E[X] =  4/8 = 1/2 since each of the sequences HHT and TTH and HTT and THH has 1 doubleton, while each of the sequences HHH and TTT and HTH and THT has 0 doubletons.)

Assume that X can be polynomially reduced  to Z, in that there exists a function f such that     forall  x,   x in X   iff   f(x) in Zand f can be computed in time polynomial in the size of x. Which inferences are then valid?

Exam 4- Chapters 14, 15, &16

Exam 1- Chapters 6, 17 & 18