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

Q. 3. (5 marks) [CLO 2] At the Business College of UMS, 800 students are enrolled in the Bachelor of Business Administration (BBA). Among them, 200 students enrolled in an Introductory Statistics course. Of these 200 students, 50 are also enrolled in an Introductory Accounting course. There are an additional 250 business students enrolled in accounting but not enrolled in statistics. If a business student is selected at random, a) What is the probability that the student is enrolled in both statistics and accounting? b) If a business student is selected at random and found to be enrolled in statistics, what is the probability that the student is also enrolled in accounting? c) If a business student is selected at random, what is the probability that the student is not enrolled in statistics?Example 3: North Carolina University posts the grade distributions for its courses online. Students in Statistics 101 in the fall 2007 semester received 26% A's, 42% B's, 20% C's, 10% D's, and 2%F's. Choose a Statistics 101 student at random. To "choose at random" means to give every student the same chance to be chosen. The student's grade on a four-point scale (with A=4) is a discrete random variableX. (a) What is the probability distribution of X? (b) Say in words what the meaning of P(X 2 3) is. What is this probability?Problem 5.28 (Page 225) The following table lists the probability distribution of the number of questions solved by students in a gee-statistics during 15 minutes. Patients per 0 l 2 3 4 5 6 hour Probability.Ir 0.2165 0.4133 0.21 [20.0998 0.0314 0.0138 0.0090 Calculate the mean and standard deviation for this probability distribution. Draw conclusion based on your result