In 1996, the General Social Survey (which uses a method similar to simple random sampling) asked, “On the whole, do you think it should be the government’s responsibility to provide decent housing for those who can’t afford it?” For this question, 240 people said that it definitely should out of 1572 randomly selected people. We will make a 90% confidence interval for:

a. p, the true population proportion that would have answered yes to this question

b. p, the sample proportion that answered yes to this question

c. p-hat, the sample proportion that answered yes to this question

d. p-hat, the true population proportion that would have answered yes to this question

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In 1996, the General Social Survey (which uses a method similar to simple random sampling) asked, “On the whole, do you think it should be the government’s responsibility to provide decent housing for those who can’t afford it?” For this question, 240 people said that it definitely should out of 1572 randomly selected people.  The General Social survey randomly selects adults living in the US. Someone wanted to compute a 95% confidence interval for p.

What is the parameter?

Group of answer choices

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in 1996, 32%of US households owned a personal computer. In a recent sample of 850 US households, 305 own personal computers.Test at the 2% siginificance level whether the current percentage of all U.S. households who own personal computers is different from 32%/

A. State the null and alternative hypotheses.

B. State your conclusion mathematically and state the reason why

C. State your conclusion in terms of the problem

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1.     In 1994, O. J. Simpson, an actor and former professional American football player, was accused of murdering his ex-wife, Nicole Brown Simpson. News of this court case filled the media for months. During the trial, Alan Dershowitz, an advisor to Simpson’s defence attorneys, claimed that Simpson’s previous accusation of spousal abuse was not particularly relevant. The evidence was that only about one in 2500 men who batter their significant others (wives, girlfriends) go on to kill them.  This statement went unchallenged at the trial, but was subsequently corrected in a letter to the editor in Nature in 1995. In 1994, there were approximately 125,000,000 women in the USA. That year there were approximately 3,500,000 women who were battered. There were approximately 5,000 women murdered. Approximately 1,400 women were murdered by the man who battered them.

a)     What is the probability that a woman was battered in 1994?

b)    What is the probability that a woman was murdered in 1994?

c)     The defence argued that the probability of a woman being murdered by her batterer, given she was battered was 1 in 2,500, so the fact that O.J. Simpson battered his wife was irrelevant. The prosecution should have challenged this probability because what was at issue was that Nicole Brown was murdered. Use Bayes Rule to calculate the probability that she was murdered by her batterer, given that she was murdered.

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In 2001 a company installed a new machine in one of its factories at a cost of $580,000. The machine is linearly depreciated over 24 years with a scrap value of $16,000.  Find an expression for the machine value in the tth year of use (0 < t < 24)

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