Mathematics, 17.12.2019 00:31 seymani2
Suppose x1, xm is an independent random sample of size m from a population which is normally distributed with mean my and variance 01. let y1, yn be another independent random sample of size n from a population which is normally distributed with mean uz and variance oz. let x and ỹ denote the sample means from these two samples, respectively. since the two samples are independent of each other, the corresponding sample means are also independent. (a) what are the sampling distributions of x and y ? give their names and parameters. (5 pts) (b) it is known that, both, the sum and the difference of two independent random variables that follow normal distributions are also normally distributed random variables. using this information, what are the distributions of x+y and x-y ? give their names and parameters. (hint: you just need to find the mean and variance of +7 and x-y. note, if x and y are two independent random variables, then v(x+y)=v(x)+v(y), and we know from property of variance that v(-y)=v(y)] (8 pts) (c) let oỉ =4 and oź =1, and m=32 and n=8. then, find the probability that x-y is within 1 unit of the difference in true population means u1 – m2. (5 pts)
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An energy drink company claims that its product increases students' memory levels. to support its claims, the company issues advertisements claiming that 8 out of 10 people (chosen randomly from across the country) who tried their product reported improved memory. the missing component in this study is a .
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Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.
Answers: 3
Suppose x1, xm is an independent random sample of size m from a population which is normally distri...
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