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Which of the following statements best describes the difference between a sample and a population in statistics?

The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean?

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?