Question 1
(a) (Binomial Distribution, p-value)
(b)
In 2000 a local university conducted a survey on smoking and found that 20% of its students smoked. In 2007 as the research assistant of a research project you randomly chose ten (10) students from that university and interviewed them about smoking. Answer the below questions, assuming the proportion of students who smoked was unchanged in 2007. (i) What is the expected number of students who smoke in the sample? (ii) What is the probability that two (2) of the ten students you interviewed smoke? (iii) Suppose five (5) students in the sample smoked. Can you use this sample result to conclude that the proportion of students who smoked in 2007 had increased (a = 5%)?
(Normal Distribution, Sampling Distribution) A machine produces a component with mean length 300 cm and standard deviation 25 cm. (i) Find the probability that a randomly selected component is longer than 325 cm. (ii) A random sample of 4 manufactured components is drawn and their length recorded. Find the probability that the mean length of the sample is longer than 325 cm. (iii) Suppose a random sample of 100 manufactured components is now drawn. Find the probability that the mean length of the sample is longer than 325 cm. (iv) What assumption do you have to make in part (i) & (ii)? Do you have to make the same assumption in part (iii)? Why/Why not?
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