Please place your completed assignment in the box marked for your tutorial group in the basement of BSB.
In Assignment 1, you programmed a spreadsheet to plot the Bin(n, p) p.d.f for any given n and p. Use this spreadsheet to demonstrate the Central Limit Theorem. In particular, there is a "rule of thumb" that says that the normal approximation to the binomial will be adequate if np > 5 when p < 0.5 or if nq > 5 when p > 0.5. Investigate how well this rule works. [Suggestion: Give some plots to compare the binomial p.d.f. with the normal p.d.f. Compare some binomial tail areas, computed with the spreadsheet, to approximate tail areas computed by the normal approximation. Use the continuity correction.]
Every morning from 1993-11-16 to 1995-01-19, I recorded the price per litre of regular gasoline at Sarah's Sunoco on Main Street West at Newton Avenue. Click here to get the data. (a) Draw a lag 1 scatter plot. (b) If x(i) is the price on day i, compute d(i) = x(i+1) - x(i), which is the change in price that occurred on day i. Draw a multiple box plot showing change in price by day of the week. (c) Plot any other graphical display that you think is interesting. (d) Explain what you have learned from the data.
In 1995, the Spanish trawler Estai was arrested for allegedly catching undersized turbot in Canadian waters. An article in the Hamilton Spectator reported that 79% of the turbot on board were less than 38 cm in length and 6% of the catch was less than 17 cm. Assuming a normal distribution for fish length in the catch, what are the mean and standard deviation of length? If the minimum size of a mature turbot is taken to be 60 cm, what percentage of the catch were mature turbot?
Assume that the weights of people who use a certain elevator are distributed independently and normally with a mean of 65 kg and a 10% coefficient of variation. The total capacity of the elevator is rated at 1000 kg. What is the maximum number of people the elevator can hold if the probability of exceeding the rated capacity is not to exceed 1%? Would this number be greater or less if the weights were positively correlated?
Do 6.24 to 6.28 on page 186.
The data set ENDOCRINE is described on page 342. Plot a SPLOM and the corresponding correlation matrix for the four hormones, treating the sample as 10 independent observations and again after averaging over the split-sample determinations within each subject. Which is the more valid? Explain what you have learned from the analysis.