In a study about train delays in The Netherlands one was interested in

whether arrival delays of trains exhibit more variation during rush hours than

during quiet hours. The observed arrival delays during rush hours are modeled as realizations of a random sample from a distribution with variance ?2

1,

and similarly the observed arrival delays during quiet hours correspond to a

distribution with variance ?2

2. One tests the null hypothesis H0 : ?1 = ?2.

What do you choose as the alternative hypothesis?

25.2 On average, the number of babies born in Cleveland, Ohio, in the

month of September is 1472. On January 26, 1977, the city was immobilized

by a blizzard. Nine months later, in September 1977, the recorded number of

births was 1718. Can the increase of 246 be attributed to chance? To investigate this, the number of births in the month of September is modeled by a

Poisson random variable with parameter , and we test H0 : = 1472. What

would you choose as the alternative hypothesis?

25.3 Recall Exercise 17.9 about black cherry trees. The scatterplot of y (volume) versus x = d2h (squared diameter times height) seems to indicate that

the regression line y = ? + ?x runs through the origin. One wants to investigate whether this is true by means of a testing problem. Formulate a null

hypothesis and alternative hypothesis in terms of (one of) the parameters ?

and ?

Suppose we have a dataset x1,...,xn that may be modeled as the

realization of a random sample X1,...,Xn from an Exp(?) distribution, where

? is unknown. Let Sn = X1 + + Xn.

a. Check that ?Sn has a Gam(n, 1) distribution.

b. The following quantiles of the Gam(20, 1) distribution are given: q0.05 =

13.25 and q0.95 = 27.88. Use these to construct a 90% confidence interval

for ? when

(5 points) Show that the parabolic distribution given by x2 0 4 is the claim.Qu Que Ques Quest D Question 18 2 pts Time running: Attempt due: 12 May The Starfleet Academy currently has 400 business students. Of these 400 students, 106 are currently enrolled in accounting and 107 are currently enrolled in business statistics, It is also known that 30 business students are currently enrolled in both courses, One business 1 Hour, 55 minute student is randomly selected. () What is the probability that the student was enrolled in either Business Statistics or in Accounting? PreviousBart and Lisa Simpsons take a Statistics class. The chance that Bart passes Statistics is 30%. The chance that Lisa passes Statistics is 80%. Let X be the number of Simpsons that pass Statistics. 1. Set up the table of distribution and cumulative distribution of X. (A probability tree may be helpful.) 2. Calculate the expected value and standard deviation of X. 3. How likely is it that exactly one of the two passes